Irregular total labeling of wheel related graphs

Abstract

A vertex (edge) irregular total L-labeling φof a graph G is a labeling of the vertices and edges of G with labels from the set {1,2,..., L} in such a way that any two different vertices (edges) have distinct weights. Here, the weight of a vertex x in G is the sum of the label of x and the labels of all edges incident with the vertex x, whereas the weight of an edge is the sum of label of the edge and the vertices incident to that edge. The minimum L for which the graph G has a vertex (edge) irregular total L-labeling is called the total vertex (edge) irregularity strength of G. In this paper, the exact values for the total vertex and edge irregularity strength of three wheel related families of graphs have been determined. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.