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On edge irregularity strength of Toeplitz graphs

Abstract:

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.