Locating Edge Domination Number of Some Classes of Claw-Free Cubic Graphs

Let G=V;E be a simple graph with vertex set V and edge set E. In a graph G, a subset of edges denoted by M is referred to as an edge-dominating set of G if every edge that is not in M is incident to at least one member of M. A set M subset of E is the locating edge-dominating set if for every two edges e1,e2 is an element of E-M, the sets Ne1 boolean AND M and Ne2 boolean AND M are nonempty and different. The edge domination number gamma LG of G is the minimum cardinality of all edge-dominating sets of G. The purpose of this study is to determine the locating edge domination number of certain types of claw-free cubic graphs.