Dominating and Locating Sets in the Multiplication of a Graph

P  Inpoonjai   and T  Jiarasuksakun

doi:10.17485/ijst/2015/v8i32/92121

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Dominating and Locating Sets in the Multiplication of a Graph

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i32/92121

Year: 2015, Volume: 8, Issue: 32, Pages: 1-6

Original Article

Dominating and Locating Sets in the Multiplication of a Graph

P. Inpoonjai^1* and T. Jiarasuksakun²

¹Faculty of Sciences and Agricultural Technology, Rajamangala University of Technology Lanna Chiangrai, 99, Sai Khao, Phan District, Chiang Rai, 57120, Thailand; [email protected]
²Department 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]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

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