Isnaini Rosyida, Mulyono, Diari Indriati
We presume that G(V, E) is a simple, undirected, and connected graph. A function ? 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. © 2021 Author(s).
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Semarang, Semarang, Indonesia; Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Surakarta, Indonesia
