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: | 24 Mar 2021 14:17 |
| URI: | http://repository.ubaya.ac.id/id/eprint/274 |
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