Abstract
A subset D of V(G) is called a vertex dominating set of G if every vertex not in D is adjacent to some vertices in D. A graph G = (V, E) is called a locating dominating set if for every two vertices . Locating dominating number is the minimum cardinality of a locating dominating set. The value of locating domination number is . Edge comb product denoted by is a graph obtained by taking one copy of G and |E(G)| copies of H and grafting the i-th copy of H at the edge e to the i-th edge of G. This paper studies about locating domination number in edge comb product graph where G is path graph Pn and H is complete graph Km, star graph Sm, triangular book graph BTm, path graph Pm, friendship graph and fan graph Fm.
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