Total irregularity strength of disjoint union of crossed prism and necklace graphs

Abstract

A totally irregular total k-labeling f: VJE-{1,2,3,..., k is a labeling of vertices and edges of G in such a way that for any two different vertices x and y their vertex-weights wt(x) ∗ wt(y) where the vertex-weight wt(x) = + Z and also for every two different edges xy and xy of G their jsc£ edge-weights wtf(x¹y¹) = f(x) + f(x¹y¹) + f(y) and wtj{xy)-f(x1) + f(x¹y¹)) + () are distinct. A total irregularity strength of graph G, denoted by ts(G) is defined as the minimum k for which a graph G has a totally irregular total c-labeling. In this paper, we investigate the total irregularity strength of the crossed prism, m copies of crossed prism, necklace and m copies of necklace. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.