Generalized spectral characterizations of a new family of noncontrollable graphs

Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e ,...
Ausführliche Beschreibung

Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n . Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Qiu, Lihong [verfasserIn] Qiu, Guangkun [verfasserIn] Mao, Lihuan [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Noncontrollable graph Generalized spectrum Determined by spectrum Rational orthogonal matrix

Übergeordnetes Werk:	Enthalten in: Linear algebra and its applications - New York, NY : American Elsevier Publ., 1968, 683, Seite 211-234
Übergeordnetes Werk:	volume:683 ; pages:211-234

DOI / URN:	10.1016/j.laa.2023.12.006

Katalog-ID:	ELV066313554

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520			\|a Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n .
650		4	\|a Noncontrollable graph
650		4	\|a Generalized spectrum
650		4	\|a Determined by spectrum
650		4	\|a Rational orthogonal matrix
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700	1		\|a Mao, Lihuan \|e verfasserin \|4 aut
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936	b	k	\|a 31.25 \|j Lineare Algebra \|j multilineare Algebra \|q VZ
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allfields	10.1016/j.laa.2023.12.006 doi (DE-627)ELV066313554 (ELSEVIER)S0024-3795(23)00456-1 DE-627 ger DE-627 rda eng 510 VZ 31.25 bkl Qiu, Lihong verfasserin aut Generalized spectral characterizations of a new family of noncontrollable graphs 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n . Noncontrollable graph Generalized spectrum Determined by spectrum Rational orthogonal matrix Qiu, Guangkun verfasserin aut Mao, Lihuan verfasserin aut Enthalten in Linear algebra and its applications New York, NY : American Elsevier Publ., 1968 683, Seite 211-234 Online-Ressource (DE-627)266882374 (DE-600)1468081-6 (DE-576)078315026 nnns volume:683 pages:211-234 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.25 Lineare Algebra multilineare Algebra VZ AR 683 211-234
spelling	10.1016/j.laa.2023.12.006 doi (DE-627)ELV066313554 (ELSEVIER)S0024-3795(23)00456-1 DE-627 ger DE-627 rda eng 510 VZ 31.25 bkl Qiu, Lihong verfasserin aut Generalized spectral characterizations of a new family of noncontrollable graphs 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n . Noncontrollable graph Generalized spectrum Determined by spectrum Rational orthogonal matrix Qiu, Guangkun verfasserin aut Mao, Lihuan verfasserin aut Enthalten in Linear algebra and its applications New York, NY : American Elsevier Publ., 1968 683, Seite 211-234 Online-Ressource (DE-627)266882374 (DE-600)1468081-6 (DE-576)078315026 nnns volume:683 pages:211-234 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.25 Lineare Algebra multilineare Algebra VZ AR 683 211-234
allfields_unstemmed	10.1016/j.laa.2023.12.006 doi (DE-627)ELV066313554 (ELSEVIER)S0024-3795(23)00456-1 DE-627 ger DE-627 rda eng 510 VZ 31.25 bkl Qiu, Lihong verfasserin aut Generalized spectral characterizations of a new family of noncontrollable graphs 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n . Noncontrollable graph Generalized spectrum Determined by spectrum Rational orthogonal matrix Qiu, Guangkun verfasserin aut Mao, Lihuan verfasserin aut Enthalten in Linear algebra and its applications New York, NY : American Elsevier Publ., 1968 683, Seite 211-234 Online-Ressource (DE-627)266882374 (DE-600)1468081-6 (DE-576)078315026 nnns volume:683 pages:211-234 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.25 Lineare Algebra multilineare Algebra VZ AR 683 211-234
allfieldsGer	10.1016/j.laa.2023.12.006 doi (DE-627)ELV066313554 (ELSEVIER)S0024-3795(23)00456-1 DE-627 ger DE-627 rda eng 510 VZ 31.25 bkl Qiu, Lihong verfasserin aut Generalized spectral characterizations of a new family of noncontrollable graphs 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n . Noncontrollable graph Generalized spectrum Determined by spectrum Rational orthogonal matrix Qiu, Guangkun verfasserin aut Mao, Lihuan verfasserin aut Enthalten in Linear algebra and its applications New York, NY : American Elsevier Publ., 1968 683, Seite 211-234 Online-Ressource (DE-627)266882374 (DE-600)1468081-6 (DE-576)078315026 nnns volume:683 pages:211-234 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.25 Lineare Algebra multilineare Algebra VZ AR 683 211-234
allfieldsSound	10.1016/j.laa.2023.12.006 doi (DE-627)ELV066313554 (ELSEVIER)S0024-3795(23)00456-1 DE-627 ger DE-627 rda eng 510 VZ 31.25 bkl Qiu, Lihong verfasserin aut Generalized spectral characterizations of a new family of noncontrollable graphs 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n . Noncontrollable graph Generalized spectrum Determined by spectrum Rational orthogonal matrix Qiu, Guangkun verfasserin aut Mao, Lihuan verfasserin aut Enthalten in Linear algebra and its applications New York, NY : American Elsevier Publ., 1968 683, Seite 211-234 Online-Ressource (DE-627)266882374 (DE-600)1468081-6 (DE-576)078315026 nnns volume:683 pages:211-234 GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.25 Lineare Algebra multilineare Algebra VZ AR 683 211-234
language	English
source	Enthalten in Linear algebra and its applications 683, Seite 211-234 volume:683 pages:211-234
sourceStr	Enthalten in Linear algebra and its applications 683, Seite 211-234 volume:683 pages:211-234
format_phy_str_mv	Article
bklname	Lineare Algebra multilineare Algebra
institution	findex.gbv.de
topic_facet	Noncontrollable graph Generalized spectrum Determined by spectrum Rational orthogonal matrix
dewey-raw	510
isfreeaccess_bool	false
container_title	Linear algebra and its applications
authorswithroles_txt_mv	Qiu, Lihong @@aut@@ Qiu, Guangkun @@aut@@ Mao, Lihuan @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	266882374
dewey-sort	3510
id	ELV066313554
language_de	englisch
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author	Qiu, Lihong
spellingShingle	Qiu, Lihong ddc 510 bkl 31.25 misc Noncontrollable graph misc Generalized spectrum misc Determined by spectrum misc Rational orthogonal matrix Generalized spectral characterizations of a new family of noncontrollable graphs
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topic_title	510 VZ 31.25 bkl Generalized spectral characterizations of a new family of noncontrollable graphs Noncontrollable graph Generalized spectrum Determined by spectrum Rational orthogonal matrix
topic	ddc 510 bkl 31.25 misc Noncontrollable graph misc Generalized spectrum misc Determined by spectrum misc Rational orthogonal matrix
topic_unstemmed	ddc 510 bkl 31.25 misc Noncontrollable graph misc Generalized spectrum misc Determined by spectrum misc Rational orthogonal matrix
topic_browse	ddc 510 bkl 31.25 misc Noncontrollable graph misc Generalized spectrum misc Determined by spectrum misc Rational orthogonal matrix
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Generalized spectral characterizations of a new family of noncontrollable graphs
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title_full	Generalized spectral characterizations of a new family of noncontrollable graphs
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title_sort	generalized spectral characterizations of a new family of noncontrollable graphs
title_auth	Generalized spectral characterizations of a new family of noncontrollable graphs
abstract	Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n .
abstractGer	Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n .
abstract_unstemmed	Let G be an n-vertex graph with adjacency matrix A and let e be the all-one vector. Then the walk matrix of G is defined as W = [ e , A e , A 2 e , … , A n − 1 e ] . We call G controllable if the rank of W is n and noncontrollable otherwise. A graph G is determined by the generalized spectrum, DGS for short, if any graph H having the same generalized spectrum as G must be isomorphic to G. In Wang , the author proposed a method for a family of controllable graphs to be DGS. However, the method fails for noncontrollable graphs, and it turns out that proving a noncontrollable graph to be DGS is more difficult than proving a controllable graph to be DGS. Up to now, there are just a few attempts to investigate generalized spectral characterizations of noncontrollable graphs for which the rank of W is n − 1 . In this paper, we focus on spectral characterizations of a new family of noncontrollable graphs for which the rank of W is n − 2 , denoted by G n . We present an arithmetic criterion to determine whether a given graph is DGS in G n .
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title_short	Generalized spectral characterizations of a new family of noncontrollable graphs
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up_date	2024-07-06T17:19:06.736Z
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Generalized spectral characterizations of a new family of noncontrollable graphs

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