On The LDS of the Joint Product of Graphs

Abstract

Locating dominating set (LDS) is one of the topics of graph theory. A set VD of vertices in graph G is called a dominating set if every vertex V u is either an element of D or adjacent to some element of D [3]. The domination number is the minimum cardinality of dominating set and denoted by .G Domination set D in graph EV G , is a locating dominating set if for each pair of distinct vertices u and v in D GV we have

uN vND ,D

and N I

,D vN I where uN is the neighboring set of u. Locating domination number which is denoted by GL is the minimum cardinality of locating dominating set [4]. This research aims to determine locating dominating set of some joint product of graphs and its relation with its basis graphs. Simple graphs used here are star graph, helm graph, triangular book graph and prism graph.