# Location-2-domination for product of graphs

01 Jan 2019-pp 507-515

TL;DR: In this paper, the Location-2-domination number for direct and Cartesian product of graphs is denoted as R 2 G (G) (R = 2 G(G), where G is the number of vertices in a graph.

Abstract: Locating-2-Dominating Set is denoted as \(R_{2}^{D}(G)\), and in this chapter the Location-2-domination number for direct and Cartesian product of graphs, namely \({{P}_{n}}\square {{P}_{m}}\), \({{P}_{n}}\square {{S}_{m}}\), \({{P}_{n}}\square {{W}_{m}}\), \({{C}_{n}}\square {{C}_{m}}\), Pn × Pm, Pn × Sm, Cn × Pm, Cn × Cm, are being found.

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01 Jan 1998

TL;DR: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms are presented.

Abstract: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms.

3,265 citations

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TL;DR: Sharp bounds on the cardinality of locating-dominating sets for arbitrary graphs on p vertices and for trees on p trees are given, and a linear algorithm for finding a minimum cardinality locating-Dominating set in an acyclic graph is presented.

Abstract: Locating-dominating sets are of interest in safeguard applications of graphical models of facilities. A subset S of the vertex set V of a graph G is a dominating set if each vertex u ϵ V - S is adjacent to at least one vertex in S. For each v in V - S let S(v) denote the set of vertices in S which are adjacent to v. A dominating set S is defined to be “locating” if for any two vertices v and w in V - S one has S(v) ≠ S(w). Sharp bounds on the cardinality of locating-dominating sets for arbitrary graphs on p vertices and for trees on p vertices are given, and a linear (that is O(P)) algorithm for finding a minimum cardinality locating-dominating set in an acyclic graph is presented.

211 citations