## ON TOTAL VERTEX IRREGULARITY STRENGTH OF SOME CLASSES OF TADPOLE CHAIN GRAPHS

## ON TOTAL VERTEX IRREGULARITY STRENGTH OF SOME CLASSES OF TADPOLE CHAIN GRAPHS

*I. Rosyida, D. Indriati*

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## Abstract

A total k-labeling f that assigns V ∪ E into {1, 2, . . . , k} on graph G is named vertex irregular if wtf(u) ̸= wtf(v) for dissimilar vertices u,v in G with the weights wtf (u) = f(u) + ux∈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 con- tain tadpole graphs in their blocks. We investigate tvs of some classes of tadpole chain graphs,. i.e., Tr(4,n) and Tr(5,n) with length r. Some formulas are derived as follows:

## Keywords

Vertex irregular total k-labeling, tvs, tadpole graph, chain graph.