Edge irregularity strength of some rooted product graphs

Abstract

We determine a graph parameter called edge irregularity strength es(G) i.e least value k such that there is a function f : V(G)→{1, 2, 3, 4, . . . ,k} of vertices of graph from which weights of edges are different for every pair of edges. Weight of an edge is the sum of the labels of end vertices i.e Wf(uv) = f(u)+f(v) for every uv E(G). A vertex k-labeling is defined as an edge irregular k labeling of graph G if for every two different edges a and b their weights are different i.e Wf(a) ≠Wj((b). In this paper we estimate the bounds of the edge irregularity strength and calculate the accurate value for some families of graphs. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.