On the total irregularity strength of wheel related graphs

Abstract

A totally irregular total k-labeling f: VUE (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 wth(x) wth{y) where the vertex-weight wtn(x) = Z Kz) and also for every two different edges xy and x'y' of G their edge-weights wth(xy) = A(jc) + h(xy) + h(y) and wfo(jcy) = h{xf) + h(x/y') + h{y') 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 ^-labeling. In this paper, we investigate some wheel related graphs whose total irregularity strength equals to the lower bound. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.