On global (strong) defensive alliances in some product graphs

Autor: Ismael Gonz\'alez Yero, ‎Marko Jakovac$, Dorota Kuziak
Jazyk: angličtina
Rok vydání: 2017
Předmět:
Zdroj: Communications in Combinatorics and Optimization, Vol 2, Iss 1, Pp 21-33 (2017)
Druh dokumentu: article
ISSN: 2538-2128
2538-2136
DOI: 10.22049/CCO.2017.13595
Popis: 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.
Databáze: Directory of Open Access Journals