On totally irregular total labeling of caterpillars having even number of internal vertices with degree three
Isnaini Anniswati Rosyida, Mulyono Mulyono, Diari Indriati · AIP conference proceedings · 2021
We presume that G(V, E) is a simple, undirected, and connected graph. A function λ from V ∪ E to {1, 2,…, k} is named a totally irregular total k-labeling if the set of vertex-weights and the set of edge-weights of G consist of different values. The minimum integer k in such a way that G has a totally irregular total k-labeling is mentioned as total irregularity strength of G, denoted by ts(G). We investigate the total irregularity strength of the caterpillars that have an even number of internal vertices with degree three. The results are as follows: ts(Sn,3,3,…,3,︸tSn)=2n+(t−1)2 and ts(Sm−1,3,3,…,3,︸tSm)=2m+(t−1)2 for even number t.