Total irregularity strength of cycle related graphs with pendent edges

Let G = (V, E) be a graph. A total labeling psi : V boolean OR E -> {1, 2, ... , k} is called totally irregular total k-labeling of G if every two distinct vertices u and v in V (G) satisfy wt(u) not equal wt(v), and every two distinct edges u(1)u(2) and v(1)v(2) in E(G) satisfy wt(u(1)u(2)) not equal wt(v(1)v(2)), where wt(u) = psi(u) + Sigma(uv is an element of E(G)) psi(uv) and wt(u(1)u(2)) = psi(u1) + psi(u(1)u(2)) + psi(u(2)). 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 determine the exact value of the total irregularity strength of cycle related graphs (convex polytopes) with pendent edges.