Abstract

A locating-dominating set of a graph G is a dominating set of G such that every vertex of G outside the dominating set is uniquely identified by its neighborhood within the dominating set. The location-domination number of G is the minimum cardinality of a locating-dominating set in G. Let G1 and G2 be two disjoint copies of a graph G and f:V(G1)→V(G2) be a function. A functigraph FGf consists of vertex set V(G1)∪V(G2) and edge set E(G1)∪E(G2)∪{uv:v=f(u)}. In this paper, we study the variation of location-domination number in passing from G to FGf and find its sharp lower and upper bounds. We also study location-domination number of functigraphs of complete graphs for all possible definitions of function f. We also obtain location-domination number of functigraphs of a family of spanning subgraph of the complete graphs.

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