Abstract
Let G = (V, E) be a graph. A total labeling phi : V boolean OR E -> {1, 2,..., k} is called totally irregular total k-labeling of G if every two distinct vertices x and y in V(G) satisfies wt(x) not equal wt(y), and every two distinct edges xy and x'y' in E(G) satisfies wt(xy) not equal wt(x' y'), where wt(x) = phi(x) + Sigma(xz is an element of E(G)) phi(xz) and wt(xy) = phi(x) + phi(xy)) + phi(y). The minimum k for which a graph G has a totally irregular total k-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.