On the fractional strong metric dimension of graphs
For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong re...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kang, Cong X. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016transfer abstract |
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| Schlagwörter: |
Mutually maximally distant (MMD) vertices |
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| Umfang: |
9 |
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| Übergeordnetes Werk: |
Enthalten in: Electroless deposition of a Ag matrix on semiconducting one-dimensional nanostructures - Miguel, F.L. ELSEVIER, 2013transfer abstract, [S.l.] |
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| Übergeordnetes Werk: |
volume:213 ; year:2016 ; day:20 ; month:11 ; pages:153-161 ; extent:9 |
| Links: |
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| DOI / URN: |
10.1016/j.dam.2016.05.027 |
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ELV029588065 |
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| 520 | |a For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . | ||
| 520 | |a For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . | ||
| 650 | 7 | |a Orbit-stabilizer equation |2 Elsevier | |
| 650 | 7 | |a Mutually maximally distant (MMD) vertices |2 Elsevier | |
| 650 | 7 | |a Fractional (strong) metric dimension |2 Elsevier | |
| 650 | 7 | |a (Strong) metric dimension |2 Elsevier | |
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10.1016/j.dam.2016.05.027 doi GBVA2016005000029.pica (DE-627)ELV029588065 (ELSEVIER)S0166-218X(16)30252-9 DE-627 ger DE-627 rakwb eng 510 510 DE-600 070 VZ 660 VZ 333.7 610 VZ 43.12 bkl 43.13 bkl 44.13 bkl Kang, Cong X. verfasserin aut On the fractional strong metric dimension of graphs 2016transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . Orbit-stabilizer equation Elsevier Mutually maximally distant (MMD) vertices Elsevier Fractional (strong) metric dimension Elsevier (Strong) metric dimension Elsevier Enthalten in Elsevier Miguel, F.L. ELSEVIER Electroless deposition of a Ag matrix on semiconducting one-dimensional nanostructures 2013transfer abstract [S.l.] (DE-627)ELV011300345 volume:213 year:2016 day:20 month:11 pages:153-161 extent:9 https://doi.org/10.1016/j.dam.2016.05.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-GGO GBV_ILN_20 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 43.12 Umweltchemie VZ 43.13 Umwelttoxikologie VZ 44.13 Medizinische Ökologie VZ AR 213 2016 20 1120 153-161 9 045F 510 |
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10.1016/j.dam.2016.05.027 doi GBVA2016005000029.pica (DE-627)ELV029588065 (ELSEVIER)S0166-218X(16)30252-9 DE-627 ger DE-627 rakwb eng 510 510 DE-600 070 VZ 660 VZ 333.7 610 VZ 43.12 bkl 43.13 bkl 44.13 bkl Kang, Cong X. verfasserin aut On the fractional strong metric dimension of graphs 2016transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . Orbit-stabilizer equation Elsevier Mutually maximally distant (MMD) vertices Elsevier Fractional (strong) metric dimension Elsevier (Strong) metric dimension Elsevier Enthalten in Elsevier Miguel, F.L. ELSEVIER Electroless deposition of a Ag matrix on semiconducting one-dimensional nanostructures 2013transfer abstract [S.l.] (DE-627)ELV011300345 volume:213 year:2016 day:20 month:11 pages:153-161 extent:9 https://doi.org/10.1016/j.dam.2016.05.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-GGO GBV_ILN_20 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 43.12 Umweltchemie VZ 43.13 Umwelttoxikologie VZ 44.13 Medizinische Ökologie VZ AR 213 2016 20 1120 153-161 9 045F 510 |
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10.1016/j.dam.2016.05.027 doi GBVA2016005000029.pica (DE-627)ELV029588065 (ELSEVIER)S0166-218X(16)30252-9 DE-627 ger DE-627 rakwb eng 510 510 DE-600 070 VZ 660 VZ 333.7 610 VZ 43.12 bkl 43.13 bkl 44.13 bkl Kang, Cong X. verfasserin aut On the fractional strong metric dimension of graphs 2016transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . Orbit-stabilizer equation Elsevier Mutually maximally distant (MMD) vertices Elsevier Fractional (strong) metric dimension Elsevier (Strong) metric dimension Elsevier Enthalten in Elsevier Miguel, F.L. ELSEVIER Electroless deposition of a Ag matrix on semiconducting one-dimensional nanostructures 2013transfer abstract [S.l.] (DE-627)ELV011300345 volume:213 year:2016 day:20 month:11 pages:153-161 extent:9 https://doi.org/10.1016/j.dam.2016.05.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-GGO GBV_ILN_20 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 43.12 Umweltchemie VZ 43.13 Umwelttoxikologie VZ 44.13 Medizinische Ökologie VZ AR 213 2016 20 1120 153-161 9 045F 510 |
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10.1016/j.dam.2016.05.027 doi GBVA2016005000029.pica (DE-627)ELV029588065 (ELSEVIER)S0166-218X(16)30252-9 DE-627 ger DE-627 rakwb eng 510 510 DE-600 070 VZ 660 VZ 333.7 610 VZ 43.12 bkl 43.13 bkl 44.13 bkl Kang, Cong X. verfasserin aut On the fractional strong metric dimension of graphs 2016transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . Orbit-stabilizer equation Elsevier Mutually maximally distant (MMD) vertices Elsevier Fractional (strong) metric dimension Elsevier (Strong) metric dimension Elsevier Enthalten in Elsevier Miguel, F.L. ELSEVIER Electroless deposition of a Ag matrix on semiconducting one-dimensional nanostructures 2013transfer abstract [S.l.] (DE-627)ELV011300345 volume:213 year:2016 day:20 month:11 pages:153-161 extent:9 https://doi.org/10.1016/j.dam.2016.05.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-GGO GBV_ILN_20 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 43.12 Umweltchemie VZ 43.13 Umwelttoxikologie VZ 44.13 Medizinische Ökologie VZ AR 213 2016 20 1120 153-161 9 045F 510 |
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10.1016/j.dam.2016.05.027 doi GBVA2016005000029.pica (DE-627)ELV029588065 (ELSEVIER)S0166-218X(16)30252-9 DE-627 ger DE-627 rakwb eng 510 510 DE-600 070 VZ 660 VZ 333.7 610 VZ 43.12 bkl 43.13 bkl 44.13 bkl Kang, Cong X. verfasserin aut On the fractional strong metric dimension of graphs 2016transfer abstract 9 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . Orbit-stabilizer equation Elsevier Mutually maximally distant (MMD) vertices Elsevier Fractional (strong) metric dimension Elsevier (Strong) metric dimension Elsevier Enthalten in Elsevier Miguel, F.L. ELSEVIER Electroless deposition of a Ag matrix on semiconducting one-dimensional nanostructures 2013transfer abstract [S.l.] (DE-627)ELV011300345 volume:213 year:2016 day:20 month:11 pages:153-161 extent:9 https://doi.org/10.1016/j.dam.2016.05.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-GGO GBV_ILN_20 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 43.12 Umweltchemie VZ 43.13 Umwelttoxikologie VZ 44.13 Medizinische Ökologie VZ AR 213 2016 20 1120 153-161 9 045F 510 |
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on the fractional strong metric dimension of graphs |
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For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . |
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For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . |
| abstract_unstemmed |
For any two vertices x and y of a graph G , let S { x , y } denote the set of vertices z such that either x lies on a y − z geodesic or y lies on an x − z geodesic. For a function g defined on V ( G ) and U ⊆ V ( G ) , let g ( U ) = ∑ x ∈ U g ( x ) . A function g : V ( G ) → [ 0 , 1 ] is a strong resolving function of G if g ( S { x , y } ) ≥ 1 , for every pair of distinct vertices x , y of G . The fractional strong metric dimension, s d i m f ( G ) , of a graph G is min { g ( V ( G ) ) : g is a strong resolving function of G } . This paper furthers the study of fractional strong metric dimension initiated in COCOA 2013 (Lecture Notes in Comput. Sci.). First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. Finally, motivated by the work of Arumugam, Mathew, and Shen, we describe a class of graphs G for which s d i m f ( G ) = | V ( G ) | 2 . |
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First, we clarify or correct the proofs to two characterization theorems contained in two papers on fractional (strong) metric dimension. Next, results on fractional strong metric dimension analogous to the work of Feng, Lv, and Wang on fractional metric dimension are offered. We provide new upper and lower bounds on s d i m f ( G ) , partly in analogy with the work done by Feng et al. and partly by exploiting the particular nature of the strong metric dimension. 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