The total edge irregular strength of the path union of cycles

Abstract

For a simple graph G = (V,E) with the vertex set V and the edge set E, a labeling μ : V U E → {1,2,3,..., k} is called an edge irregular total k-labelling of G if for any two different edges e = uv and e' = u'v' in E(G) we have wt(e) = wt(e') where wt(e) = μ(u) + μ (e) + μ (v) and wt (e') = μ (u') + μ (e') + μ (v'). The total edge irregular strength tes (G) of G is the smallest positive integer k for which G has an edge irregular total k -labelling. In this paper the total edge irregular strengths of a new family of graphs, the path union of m copies of C_n is denoted by G_n,m have been determined. © 2017 Utilitas Mathematica Publishing Inc.. All rights reserved.