On the reflexive edge strength of the circulant graphs

A labeling of a graph is an assignment that carries some sets of graph elements into numbers (usually the non negative integers). The total k-labeling is an assignment f(e) from the edge set to the set {1, 2, ..., k(e)} and assignment f(v) from the vertex set to the set {0, 2, 4, ..., 2k(v)}, where k = max{k(e), 2k(v)}. An edge irregular reflexive k-labeling of the graph G is the total k-labeling, if distinct edges have distinct weights, where the edge weight is defined as the sum of label of that edge and the labels of the end vertices. The minimum k for which the graph G has an edge irregular reflexive k-labeling is called the reflexive edge strength of the graph G, denoted by re s(G). In this paper we study the edge reflexive irregular k-labeling for some cases of circulant graphs and determine the exact value of the reflexive edge strength for several classes of circulant graphs.