Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs
Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connecti...
Ausführliche Beschreibung
Autor*in: |
L. Volkmann [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2016 |
---|
Schlagwörter: |
---|
Übergeordnetes Werk: |
In: Communications in Combinatorics and Optimization - Azarbaijan Shahide Madani University, 2017, 1(2016), 1, Seite 13 |
---|---|
Übergeordnetes Werk: |
volume:1 ; year:2016 ; number:1 ; pages:13 |
Links: |
Link aufrufen |
---|
DOI / URN: |
10.22049/CCO.2016.13514 |
---|
Katalog-ID: |
DOAJ048445304 |
---|
LEADER | 01000caa a22002652 4500 | ||
---|---|---|---|
001 | DOAJ048445304 | ||
003 | DE-627 | ||
005 | 20230308134328.0 | ||
007 | cr uuu---uuuuu | ||
008 | 230227s2016 xx |||||o 00| ||eng c | ||
024 | 7 | |a 10.22049/CCO.2016.13514 |2 doi | |
035 | |a (DE-627)DOAJ048445304 | ||
035 | |a (DE-599)DOAJ220368d56ab54db1b07dbec08759b900 | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng | ||
050 | 0 | |a QA1-939 | |
100 | 0 | |a L. Volkmann |e verfasserin |4 aut | |
245 | 1 | 0 | |a Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs |
264 | 1 | |c 2016 | |
336 | |a Text |b txt |2 rdacontent | ||
337 | |a Computermedien |b c |2 rdamedia | ||
338 | |a Online-Ressource |b cr |2 rdacarrier | ||
520 | |a Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. | ||
650 | 4 | |a Digraphs | |
650 | 4 | |a Edge-connectivity | |
650 | 4 | |a Maximal edge-connected digraphs | |
650 | 4 | |a zeroth-order general Randi\'{c} index | |
653 | 0 | |a Mathematics | |
773 | 0 | 8 | |i In |t Communications in Combinatorics and Optimization |d Azarbaijan Shahide Madani University, 2017 |g 1(2016), 1, Seite 13 |w (DE-627)1017806764 |x 25382136 |7 nnns |
773 | 1 | 8 | |g volume:1 |g year:2016 |g number:1 |g pages:13 |
856 | 4 | 0 | |u https://doi.org/10.22049/CCO.2016.13514 |z kostenfrei |
856 | 4 | 0 | |u https://doaj.org/article/220368d56ab54db1b07dbec08759b900 |z kostenfrei |
856 | 4 | 0 | |u http://comb-opt.azaruniv.ac.ir/article_13514_0.html |z kostenfrei |
856 | 4 | 2 | |u https://doaj.org/toc/2538-2128 |y Journal toc |z kostenfrei |
856 | 4 | 2 | |u https://doaj.org/toc/2538-2136 |y Journal toc |z kostenfrei |
912 | |a GBV_USEFLAG_A | ||
912 | |a SYSFLAG_A | ||
912 | |a GBV_DOAJ | ||
951 | |a AR | ||
952 | |d 1 |j 2016 |e 1 |h 13 |
author_variant |
l v lv |
---|---|
matchkey_str |
article:25382136:2016----::ufcetodtosnhzrtodreearniidxomxm |
hierarchy_sort_str |
2016 |
callnumber-subject-code |
QA |
publishDate |
2016 |
allfields |
10.22049/CCO.2016.13514 doi (DE-627)DOAJ048445304 (DE-599)DOAJ220368d56ab54db1b07dbec08759b900 DE-627 ger DE-627 rakwb eng QA1-939 L. Volkmann verfasserin aut Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. Digraphs Edge-connectivity Maximal edge-connected digraphs zeroth-order general Randi\'{c} index Mathematics In Communications in Combinatorics and Optimization Azarbaijan Shahide Madani University, 2017 1(2016), 1, Seite 13 (DE-627)1017806764 25382136 nnns volume:1 year:2016 number:1 pages:13 https://doi.org/10.22049/CCO.2016.13514 kostenfrei https://doaj.org/article/220368d56ab54db1b07dbec08759b900 kostenfrei http://comb-opt.azaruniv.ac.ir/article_13514_0.html kostenfrei https://doaj.org/toc/2538-2128 Journal toc kostenfrei https://doaj.org/toc/2538-2136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 1 2016 1 13 |
spelling |
10.22049/CCO.2016.13514 doi (DE-627)DOAJ048445304 (DE-599)DOAJ220368d56ab54db1b07dbec08759b900 DE-627 ger DE-627 rakwb eng QA1-939 L. Volkmann verfasserin aut Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. Digraphs Edge-connectivity Maximal edge-connected digraphs zeroth-order general Randi\'{c} index Mathematics In Communications in Combinatorics and Optimization Azarbaijan Shahide Madani University, 2017 1(2016), 1, Seite 13 (DE-627)1017806764 25382136 nnns volume:1 year:2016 number:1 pages:13 https://doi.org/10.22049/CCO.2016.13514 kostenfrei https://doaj.org/article/220368d56ab54db1b07dbec08759b900 kostenfrei http://comb-opt.azaruniv.ac.ir/article_13514_0.html kostenfrei https://doaj.org/toc/2538-2128 Journal toc kostenfrei https://doaj.org/toc/2538-2136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 1 2016 1 13 |
allfields_unstemmed |
10.22049/CCO.2016.13514 doi (DE-627)DOAJ048445304 (DE-599)DOAJ220368d56ab54db1b07dbec08759b900 DE-627 ger DE-627 rakwb eng QA1-939 L. Volkmann verfasserin aut Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. Digraphs Edge-connectivity Maximal edge-connected digraphs zeroth-order general Randi\'{c} index Mathematics In Communications in Combinatorics and Optimization Azarbaijan Shahide Madani University, 2017 1(2016), 1, Seite 13 (DE-627)1017806764 25382136 nnns volume:1 year:2016 number:1 pages:13 https://doi.org/10.22049/CCO.2016.13514 kostenfrei https://doaj.org/article/220368d56ab54db1b07dbec08759b900 kostenfrei http://comb-opt.azaruniv.ac.ir/article_13514_0.html kostenfrei https://doaj.org/toc/2538-2128 Journal toc kostenfrei https://doaj.org/toc/2538-2136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 1 2016 1 13 |
allfieldsGer |
10.22049/CCO.2016.13514 doi (DE-627)DOAJ048445304 (DE-599)DOAJ220368d56ab54db1b07dbec08759b900 DE-627 ger DE-627 rakwb eng QA1-939 L. Volkmann verfasserin aut Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. Digraphs Edge-connectivity Maximal edge-connected digraphs zeroth-order general Randi\'{c} index Mathematics In Communications in Combinatorics and Optimization Azarbaijan Shahide Madani University, 2017 1(2016), 1, Seite 13 (DE-627)1017806764 25382136 nnns volume:1 year:2016 number:1 pages:13 https://doi.org/10.22049/CCO.2016.13514 kostenfrei https://doaj.org/article/220368d56ab54db1b07dbec08759b900 kostenfrei http://comb-opt.azaruniv.ac.ir/article_13514_0.html kostenfrei https://doaj.org/toc/2538-2128 Journal toc kostenfrei https://doaj.org/toc/2538-2136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 1 2016 1 13 |
allfieldsSound |
10.22049/CCO.2016.13514 doi (DE-627)DOAJ048445304 (DE-599)DOAJ220368d56ab54db1b07dbec08759b900 DE-627 ger DE-627 rakwb eng QA1-939 L. Volkmann verfasserin aut Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. Digraphs Edge-connectivity Maximal edge-connected digraphs zeroth-order general Randi\'{c} index Mathematics In Communications in Combinatorics and Optimization Azarbaijan Shahide Madani University, 2017 1(2016), 1, Seite 13 (DE-627)1017806764 25382136 nnns volume:1 year:2016 number:1 pages:13 https://doi.org/10.22049/CCO.2016.13514 kostenfrei https://doaj.org/article/220368d56ab54db1b07dbec08759b900 kostenfrei http://comb-opt.azaruniv.ac.ir/article_13514_0.html kostenfrei https://doaj.org/toc/2538-2128 Journal toc kostenfrei https://doaj.org/toc/2538-2136 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ AR 1 2016 1 13 |
language |
English |
source |
In Communications in Combinatorics and Optimization 1(2016), 1, Seite 13 volume:1 year:2016 number:1 pages:13 |
sourceStr |
In Communications in Combinatorics and Optimization 1(2016), 1, Seite 13 volume:1 year:2016 number:1 pages:13 |
format_phy_str_mv |
Article |
institution |
findex.gbv.de |
topic_facet |
Digraphs Edge-connectivity Maximal edge-connected digraphs zeroth-order general Randi\'{c} index Mathematics |
isfreeaccess_bool |
true |
container_title |
Communications in Combinatorics and Optimization |
authorswithroles_txt_mv |
L. Volkmann @@aut@@ |
publishDateDaySort_date |
2016-01-01T00:00:00Z |
hierarchy_top_id |
1017806764 |
id |
DOAJ048445304 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">DOAJ048445304</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230308134328.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230227s2016 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.22049/CCO.2016.13514</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ048445304</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJ220368d56ab54db1b07dbec08759b900</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA1-939</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">L. Volkmann</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Digraphs</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Edge-connectivity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Maximal edge-connected digraphs</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">zeroth-order general Randi\'{c} index</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Communications in Combinatorics and Optimization</subfield><subfield code="d">Azarbaijan Shahide Madani University, 2017</subfield><subfield code="g">1(2016), 1, Seite 13</subfield><subfield code="w">(DE-627)1017806764</subfield><subfield code="x">25382136</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:1</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:1</subfield><subfield code="g">pages:13</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.22049/CCO.2016.13514</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doaj.org/article/220368d56ab54db1b07dbec08759b900</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://comb-opt.azaruniv.ac.ir/article_13514_0.html</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2538-2128</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2538-2136</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_DOAJ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">1</subfield><subfield code="j">2016</subfield><subfield code="e">1</subfield><subfield code="h">13</subfield></datafield></record></collection>
|
callnumber-first |
Q - Science |
author |
L. Volkmann |
spellingShingle |
L. Volkmann misc QA1-939 misc Digraphs misc Edge-connectivity misc Maximal edge-connected digraphs misc zeroth-order general Randi\'{c} index misc Mathematics Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs |
authorStr |
L. Volkmann |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)1017806764 |
format |
electronic Article |
delete_txt_mv |
keep |
author_role |
aut |
collection |
DOAJ |
remote_str |
true |
callnumber-label |
QA1-939 |
illustrated |
Not Illustrated |
issn |
25382136 |
topic_title |
QA1-939 Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs Digraphs Edge-connectivity Maximal edge-connected digraphs zeroth-order general Randi\'{c} index |
topic |
misc QA1-939 misc Digraphs misc Edge-connectivity misc Maximal edge-connected digraphs misc zeroth-order general Randi\'{c} index misc Mathematics |
topic_unstemmed |
misc QA1-939 misc Digraphs misc Edge-connectivity misc Maximal edge-connected digraphs misc zeroth-order general Randi\'{c} index misc Mathematics |
topic_browse |
misc QA1-939 misc Digraphs misc Edge-connectivity misc Maximal edge-connected digraphs misc zeroth-order general Randi\'{c} index misc Mathematics |
format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
cr |
hierarchy_parent_title |
Communications in Combinatorics and Optimization |
hierarchy_parent_id |
1017806764 |
hierarchy_top_title |
Communications in Combinatorics and Optimization |
isfreeaccess_txt |
true |
familylinks_str_mv |
(DE-627)1017806764 |
title |
Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs |
ctrlnum |
(DE-627)DOAJ048445304 (DE-599)DOAJ220368d56ab54db1b07dbec08759b900 |
title_full |
Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs |
author_sort |
L. Volkmann |
journal |
Communications in Combinatorics and Optimization |
journalStr |
Communications in Combinatorics and Optimization |
callnumber-first-code |
Q |
lang_code |
eng |
isOA_bool |
true |
recordtype |
marc |
publishDateSort |
2016 |
contenttype_str_mv |
txt |
container_start_page |
13 |
author_browse |
L. Volkmann |
container_volume |
1 |
class |
QA1-939 |
format_se |
Elektronische Aufsätze |
author-letter |
L. Volkmann |
doi_str_mv |
10.22049/CCO.2016.13514 |
title_sort |
sufficient conditions on the zeroth-order general randi\'{c} index for maximally edge-connected digraphs |
callnumber |
QA1-939 |
title_auth |
Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs |
abstract |
Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. |
abstractGer |
Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. |
abstract_unstemmed |
Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. |
collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ |
container_issue |
1 |
title_short |
Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs |
url |
https://doi.org/10.22049/CCO.2016.13514 https://doaj.org/article/220368d56ab54db1b07dbec08759b900 http://comb-opt.azaruniv.ac.ir/article_13514_0.html https://doaj.org/toc/2538-2128 https://doaj.org/toc/2538-2136 |
remote_bool |
true |
ppnlink |
1017806764 |
callnumber-subject |
QA - Mathematics |
mediatype_str_mv |
c |
isOA_txt |
true |
hochschulschrift_bool |
false |
doi_str |
10.22049/CCO.2016.13514 |
callnumber-a |
QA1-939 |
up_date |
2024-07-03T17:49:29.677Z |
_version_ |
1803581096910127104 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">DOAJ048445304</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230308134328.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230227s2016 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.22049/CCO.2016.13514</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ048445304</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJ220368d56ab54db1b07dbec08759b900</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA1-939</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">L. Volkmann</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Sufficient conditions on the zeroth-order general Randi\'{c} index for maximally edge-connected digraphs</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi\'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi\'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Digraphs</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Edge-connectivity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Maximal edge-connected digraphs</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">zeroth-order general Randi\'{c} index</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Mathematics</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Communications in Combinatorics and Optimization</subfield><subfield code="d">Azarbaijan Shahide Madani University, 2017</subfield><subfield code="g">1(2016), 1, Seite 13</subfield><subfield code="w">(DE-627)1017806764</subfield><subfield code="x">25382136</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:1</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:1</subfield><subfield code="g">pages:13</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.22049/CCO.2016.13514</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doaj.org/article/220368d56ab54db1b07dbec08759b900</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://comb-opt.azaruniv.ac.ir/article_13514_0.html</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2538-2128</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2538-2136</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_DOAJ</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">1</subfield><subfield code="j">2016</subfield><subfield code="e">1</subfield><subfield code="h">13</subfield></datafield></record></collection>
|
score |
7.397979 |