Locating-dominating sets of functigraphs

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 G(1) and G(2) be two disjoint copies of a graph G and f : V (G(1)) -> V (G(2)) be a function. A functigraph consists of vertex set V(G(1)) boolean OR V(G(2)) and edge set E(G(1)) boolean OR E(G(2)) boolean OR{uv : v = f (u)}. In this paper, we study the variation of location-domination number in passing from G to F-G(f) 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. (C) 2019 Elsevier B.V. All rights reserved.