Partitioning a graph into defensive k-alliances
Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the verte...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yero, Ismael G. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2010 |
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| Schlagwörter: |
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| Anmerkung: |
© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Acta mathematica sinica - Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985, 27(2010), 1 vom: 15. Dez., Seite 73-82 |
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| Übergeordnetes Werk: |
volume:27 ; year:2010 ; number:1 ; day:15 ; month:12 ; pages:73-82 |
| Links: |
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| DOI / URN: |
10.1007/s10114-011-9075-1 |
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| Katalog-ID: |
OLC2062513011 |
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| 520 | |a Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. | ||
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| 700 | 1 | |a Sigarreta, José M. |4 aut | |
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10.1007/s10114-011-9075-1 doi (DE-627)OLC2062513011 (DE-He213)s10114-011-9075-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Yero, Ismael G. verfasserin aut Partitioning a graph into defensive k-alliances 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. Defensive alliances dominating sets domination isoperimetric number Bermudo, Sergio aut Rodríguez-Velázquez, Juan A. aut Sigarreta, José M. aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 27(2010), 1 vom: 15. Dez., Seite 73-82 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:27 year:2010 number:1 day:15 month:12 pages:73-82 https://doi.org/10.1007/s10114-011-9075-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4277 AR 27 2010 1 15 12 73-82 |
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10.1007/s10114-011-9075-1 doi (DE-627)OLC2062513011 (DE-He213)s10114-011-9075-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Yero, Ismael G. verfasserin aut Partitioning a graph into defensive k-alliances 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. Defensive alliances dominating sets domination isoperimetric number Bermudo, Sergio aut Rodríguez-Velázquez, Juan A. aut Sigarreta, José M. aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 27(2010), 1 vom: 15. Dez., Seite 73-82 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:27 year:2010 number:1 day:15 month:12 pages:73-82 https://doi.org/10.1007/s10114-011-9075-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4277 AR 27 2010 1 15 12 73-82 |
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10.1007/s10114-011-9075-1 doi (DE-627)OLC2062513011 (DE-He213)s10114-011-9075-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Yero, Ismael G. verfasserin aut Partitioning a graph into defensive k-alliances 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. Defensive alliances dominating sets domination isoperimetric number Bermudo, Sergio aut Rodríguez-Velázquez, Juan A. aut Sigarreta, José M. aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 27(2010), 1 vom: 15. Dez., Seite 73-82 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:27 year:2010 number:1 day:15 month:12 pages:73-82 https://doi.org/10.1007/s10114-011-9075-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4277 AR 27 2010 1 15 12 73-82 |
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10.1007/s10114-011-9075-1 doi (DE-627)OLC2062513011 (DE-He213)s10114-011-9075-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Yero, Ismael G. verfasserin aut Partitioning a graph into defensive k-alliances 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. Defensive alliances dominating sets domination isoperimetric number Bermudo, Sergio aut Rodríguez-Velázquez, Juan A. aut Sigarreta, José M. aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 27(2010), 1 vom: 15. Dez., Seite 73-82 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:27 year:2010 number:1 day:15 month:12 pages:73-82 https://doi.org/10.1007/s10114-011-9075-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4277 AR 27 2010 1 15 12 73-82 |
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10.1007/s10114-011-9075-1 doi (DE-627)OLC2062513011 (DE-He213)s10114-011-9075-1-p DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 17,1 ssgn Yero, Ismael G. verfasserin aut Partitioning a graph into defensive k-alliances 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. Defensive alliances dominating sets domination isoperimetric number Bermudo, Sergio aut Rodríguez-Velázquez, Juan A. aut Sigarreta, José M. aut Enthalten in Acta mathematica sinica Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, 1985 27(2010), 1 vom: 15. Dez., Seite 73-82 (DE-627)129236772 (DE-600)58083-1 (DE-576)091206189 1000-9574 nnns volume:27 year:2010 number:1 day:15 month:12 pages:73-82 https://doi.org/10.1007/s10114-011-9075-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4277 AR 27 2010 1 15 12 73-82 |
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Partitioning a graph into defensive k-alliances |
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Partitioning a graph into defensive k-alliances |
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Yero, Ismael G. |
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Acta mathematica sinica |
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Yero, Ismael G. Bermudo, Sergio Rodríguez-Velázquez, Juan A. Sigarreta, José M. |
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partitioning a graph into defensive k-alliances |
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Partitioning a graph into defensive k-alliances |
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Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 |
| abstractGer |
Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 |
| abstract_unstemmed |
Abstract A defensive k-alliance in a graph is a set S of vertices with the property that every vertex in S has at least k more neighbors in S than it has outside of S. A defensive k-alliance S is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) defensive k-alliances. The (global) defensive k-alliance partition number of a graph Θ = (V, E), (ψkgd (Γ)) ψkd(Γ), is defined to be the maximum number of sets in a partition of V such that each set is a (global) defensive k-alliance. We obtain tight bounds on ψkd(Θ) and ψkgd (Γ) in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $ Γ_{1} $ × $ Γ_{2} $ into (global) defensive (k1 + k2)-alliances and partitions of $ Γ_{i} $ into (global) defensive ki-alliances, i ∈ {1, 2}. © Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2011 |
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