Locating-dominating sets of functigraphs

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 G 1 and G 2 be the disjoint copies of a graph G and f :In this paper, we study the variation of the location-domination number in passing from G to F f G and find its sharp lower and upper bounds. We also study the location-domination number of functigraphs of the complete graphs for all possible definitions of the function f . We also obtain the location-domination number of functigraph of a family of spanning subgraph of the complete graphs.

On Locating-Dominating Set of Regular Graphs

“…An exact value of the locating-dominating number of comb product of any two connected graphs of order at least two has been determined by Pribadi and Saputro [15]. Murtaza et al [16] studied the locating-domination number of functigraphs of complete graphs. A study of a locatingdominating set of a graph by adding a universal vertex can be seen in [17].…”