Computing the total irregularity strength of wheel related graphs

Abstract

Let G = (V, E) be a graph. A total labeling φ: V ∩ E → {1,2,..., k} is called totally irregular total fc-labeling of G if every two distinct vertices x and y in V(G) satisfies wt(x) ≈ wt(y), and every two distinct edges xy and x'y' in E(G) satisfies wt(xy) ≈ wt(x'y'), where wt(x) = φ(x) + Σ φ(xz) and wt(xy) = φ(x) + φ(xy) + φ{y). The minimum k for which a graph G has a totally irregular total fc-labeling is called the total irregularity strength of G, denoted by ts(G). In this paper, we compute the total irregularity strength of wheel related graphs. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.