On total edge and total vertex irregularity strength of pentagon cactus chain graph with pendant vertices

Abstract

Let G(V, E) be a graph with a non-empty set of vertices V and a set of edges E. A total k-labeling f: V ∪ E → {1,2, …, k} is called an edge irregular total k-labeling if the weight of each edge is distinct, where the weight of an edge e = xy is wt(e) = f(xy) + f(x) + f(y). Whereas, f is a vertex irregular total k-labeling if the weight wt(x) ≠ wt(y) for two distinct vertices x, y of V(G) where the weight wt(x) = f(x) + ∑ υx∈E(G) f(υx).The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength (tes) of G. Further, the total vertex irregularity strength (tvs) of G is the minimum k for which G has a vertex irregular total k-labeling. In this paper, we find tes and tvs of heptagon cactus chain graph with pendants and get the results as follows: tes and tvs .