Security number of grid-like graphs
نویسندگان
چکیده
منابع مشابه
Security number of grid-like graphs
The security number of a graph is the cardinality of a smallest vertex subset of the graph such that any attack on the subset is defendable. In this paper, we determine the security number of two-dimensional cylinders and tori. This result settles a conjecture of Brigham et al. [R.C. Brigham, R.D. Dutton, S.T. Hedetniemi, Security in graphs, Discrete Appl. Math. 155 (2007) 1708–1714]. © 2009 El...
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The concepts of secure sets and security number in graphs were introduced first by Brigham et al. in 2007 as a generalization of the concept of alliances in graphs. Defensive alliances are related to the defense of a single vertex. But, in a general realistic settings, alliances should be formed so that any attack on the entire alliance or any subset of the alliance can be defended. In this sen...
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We use the link between the existence of tilings in Manhattan metric with {1}-bowls and minimum total dominating sets of Cartesian products of paths and cycles. From the existence of such a tiling, we deduce the asymptotical values of the total domination numbers of these graphs and we deduce the total domination numbers of some Cartesian products of cycles. Finally, we investigate the problem ...
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In 2001, Erwin introduced broadcast domination in graphs. It is a variant of classical domination where selected vertices may have different domination powers. The minimum cost of a dominating broadcast in a graph G is denoted γb(G). The dual of this problem is called multipacking : a multipacking is a set M ⊆ V (G) such that for any vertex v and any positive integer r, the ball of radius r aro...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2009.03.020