On the reflexive edge strength of the circulant graphs

Abstract

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 fe from the edge set to the set {1,2,...,ke} and assignment fv from the vertex set to the set {0,2,4,...,2kv}, where k=max{ke,2kv}. 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 res(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.

Keywords

• edge irregular reflexive labeling
• reflexive edge strength
• circulant graphs