Total edge irregularity strength of disjoint union of double wheel graphs

Abstract

An edge irregular total k-labeling f: V ∪ E → (1, 2, 3,... k) of a graph G = (V, E) is a labeling of vertices and edges of G in such a way that for any two different edges uv and u0v0 their weights f (u) + f (uv) + f (v) and f (u') + f (u'v') + f (v') are distinct. The total edge irregularity strength tes(G) is defined as the minimum k for which the graph G has an edge irregular total k-labeling. In this paper, we determine the total edge irregularity strength of disjoint union of p isomorphic double wheel graphs and disjoint union of p consecutive non-isomorphic double wheel graphs.