LOCATING-DOMINATING NUMBER IN (n−2)-REGULAR GRAPH AND (n−3)-REGULAR GRAPH - KADIR ABDUL GAFUR (NIM: 90113005), ANUWAR
Let G = (V,E) be a connected graph with vertex set V and the edge set E. Let W ⊆ V (G) is called a locating-dominating set for G if for every two distinct elements u,v ∈ V (G) W, we have ∅ 6= N(u) ∩ W 6= N(v) ∩ W 6= ∅. The locating-dominating number, denoted by λ(G), is the minimum cardinality of a locating-dominating set of G. The graph G is called k-regular, if every vertex of G is adjacent to k other vertices. Ignacio M. Pelayo (2012) have determined of locating-dominating number of k-regular graph of order n with k = 2 or k = n−1. In this project, we determine the locating-dominating number of (n−2)-regular graph with n ≥ 4 and (n−3)-regular graph with n ≥ 5.