ON EDGE IRREGULARITY STRENGTH OF TOEPLITZ GRAPHS

An edge irregular k-labeling of a graph G is a labeling of the vertices of G with labels from the set {1, 2,..., k} in such a way that for any two different edges xy and x'y' their weights w(xy) and w(x' y') are distinct. The weight w(xy) of an edge xy in G is the sum of the labels of the end vertices x and y. The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, denoted by es(G). In this paper, we study the edge irregular k-labeling for Toeplitz graphs and determine the exact value for several classes of Toeplitz graphs.