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Communications in Combinatorics and Optimization
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Volume Volume 2 (2017)
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Gonzalez Yero, I., Jakovac, M., Kuziak, D. (2017). On global (strong) defensive alliances in some product graphs. Communications in Combinatorics and Optimization, 2(1), 21-33. doi: 10.22049/cco.2017.13595
Ismael Gonzalez Yero; Marko Jakovac; Dorota Kuziak. "On global (strong) defensive alliances in some product graphs". Communications in Combinatorics and Optimization, 2, 1, 2017, 21-33. doi: 10.22049/cco.2017.13595
Gonzalez Yero, I., Jakovac, M., Kuziak, D. (2017). 'On global (strong) defensive alliances in some product graphs', Communications in Combinatorics and Optimization, 2(1), pp. 21-33. doi: 10.22049/cco.2017.13595
Gonzalez Yero, I., Jakovac, M., Kuziak, D. On global (strong) defensive alliances in some product graphs. Communications in Combinatorics and Optimization, 2017; 2(1): 21-33. doi: 10.22049/cco.2017.13595

On global (strong) defensive alliances in some product graphs

Article 3, Volume 2, Issue 1, Winter and Spring 2017, Page 21-33  XML PDF (441 K)
Document Type: Original paper
DOI: 10.22049/cco.2017.13595
Authors
Ismael Gonzalez Yero 1; Marko Jakovac2; Dorota Kuziak3
1University of Cadiz
2University of Maribor
3Universitat Rovira i Virgili
Abstract
A defensive alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at most one more
neighbor outside of $S$ than it has inside of $S$. A defensive alliance $S$ is called global if it forms a dominating set. The global defensive alliance number of a graph $G$ is the minimum cardinality of a global defensive alliance in $G$. In this article we study the global defensive alliances in Cartesian product graphs, strong product graphs and direct product graphs. Specifically we give several bounds for the global defensive alliance number of these graph products and express them in terms of the global defensive alliance numbers of the factor graphs.
Keywords
Defensive alliances; global defensive alliances; Cartesian product graphs; strong product graph; direct product graphs
Main Subjects
Graph theory
Statistics
Article View: 799
PDF Download: 777
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