On Locating-Dominating Set of Regular Graphs

Let G be a simple, connected, and finite graph. For every vertex v is an element of V(G), we denote by N-G (v) the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W subset of V(G) such that every two distinct vertices u, v is an element of V(G)\Wsatisfies (sic) N-G (u) boolean AND W dagger N-G (v) boolean AND W dagger(sci). A graph G is called k-regular graph if every vertex of G is adjacent to k other vertices of G. In this paper, we determine the locating-dominating number of k-regular graph of order n, where k = n - 2 or k = n - 3.