Locating and Total Dominating Sets of Direct Products of Complete Graphs

Iswadi, Hazrul (2011) Locating and Total Dominating Sets of Direct Products of Complete Graphs. Proceeding of 3rd International Conferences and Workshops on Basic and Applied Sciences 2011 (ICOWOBAS 2011). pp. 585-589. ISSN 978-979-19096-1-7

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Abstract

A set S of vertices in a graph G = (V,E) is a metric-locating-total dominating set of G if every vertex of V is adjacent to a vertex in S and for every u ≠ v in V there is a vertex x in S such that d(u,x) ≠ d(v,x). The metric-location-total domination number \gamma^M_t(G) of G is the minimum cardinality of a metric-locating-total dominating set in G. For graphs G and H, the direct product G × H is the graph with vertex set V(G) × V(H) where two vertices (x,y) and (v,w) are adjacent if and only if xv in E(G) and yw in E(H). In this paper, we determine the lower bound of the metric-location-total domination number of the direct products of complete graphs. We also determine some exact values for some direct products of two complete graphs.

Item Type: Article
Uncontrolled Keywords: metric-locating-total dominating set, metric-location-total domination number, direct product
Subjects: Q Science > Q Science (General)
Divisions: Academic Department > Department of Mathematics and Natural Science
Depositing User: Hazrul Iswadi 6179
Date Deposited: 29 Mar 2012 05:39
Last Modified: 29 Mar 2012 05:39
URI: http://repository.ubaya.ac.id/id/eprint/274

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