Indian Journal of Science and Technology
Year: 2015, Volume: 8, Issue: 32, Pages: 1-6
P. Inpoonjai1* and T. Jiarasuksakun2
1 Faculty of Sciences and Agricultural Technology, Rajamangala University of Technology Lanna Chiangrai, 99, Sai Khao, Phan District, Chiang Rai, 57120, Thailand; [email protected]
2 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand; [email protected]
A set S of vertices of a graph G is a dominating set of G if every vertex in V(G)\S is adjacent to some vertex in S, and S is a total dominating set of G if every vertex of G is adjacent to at least one vertex of S. An ordered set W of vertices of a connected graph G is a locating set for G if distinct vertices have distinct codes with respect to W. In this paper, we study the domination and location in the multiplication of a graph. We find the necessary and sufficient conditions for the dominating and locating sets in the multiplication of a graph to exist. We also determine bounds or the exact domination and location numbers of this graph.
Keywords: Dominating Set, Locating Code, Locating Set, Multiplication of Graph, Total Dominating Set
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