On total vertex irregularity strength of some classes of tadpole chain graphs

Abstract

A total k-labeling f that assigns V boolean OR E into {1,2, ...,k} on graph G is named vertex irregular if wt(f)(u) not equal wt(f)(v) for dissimilar vertices u, v in G with the weights wt(f) (u) = f(u) Sigma(ux is an element of E(G)) f (ux). We call the minimum number k utilized in total labeling f as a total vertex irregularity strength of G, symbolized by tvs(G). In this research, we focus on tadpole chain graphs that are chain graphs which contain tadpole graphs in their blocks. We investigate tvs of some classes of tadpole chain graphs,. i.e., T-r(4,n) and T-r(5,n) with length r. Some formulas are derived as follows: tvs(T-r(4, n)) = inverted right perpendicular(n + 1)r + 3/3inverted left perpendicular and tvs(T-r(5, n)) = inverted right perpendicular(n + 2)r + 3/3inverted left perpendicular.