An Edge Irregular Reflexive k−labeling of Comb Graphs with Additional 2 Pendants

Abstract

Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set and E(G) is the edge set. Let k be a natural numbers. For graph G we define a total k−labeling ρ such that the vertices of graph G are labeled with {0, 2, 4, . . . , 2kv} and the edges of graph G are labeled with {1, 2, 3, . . . , ke}, where k = max{2kv, ke}. Total k−labeling ρ called an edge irregular reflexive k− labeling if every two distinct edge of graph G have distinct edge weights, where the edge weight is defined as the sum of the label of that edge and the label of the vertices that are incident to this edge. The minimum k such that G has an edge irregular reflexive k−labeling called the reflexive edge strength of G. In this paper we determine the reflexive edge strength of some comb graphs.