Authors : Corry Corazon Marzuki, Fitri Aryani, Rado Yendra and Ahmad Fudholi
Abstract: A vertex irregular total k-labeling of a graph G (V, E) with a non-empty set V of vertices and a set E of edges is a labeling λ: V∪ E→{1,2, …, k} such that for every two distinct vertices have different weight. The weight of a vertex v, under a total labeling λ is the sum of label of vertex v and all labels of edges that incident with v. In other word, wt (x) = λ (x)+Σux∈Eλ (ux). The total vertex irregularity strength, denoted by tvs(G) is the minimum biggest label that use to label graph G with the vertex irregular total labeling. Some classes of graphs have been obtained its total vertex irregularity strength. In this study, researcher observe about the total vertex irregularity strength of comb product graph of Pm and Cn, denoted by TVs (Pm▹Cn). The result of this research is tvs(Pm▹Cn) = ⌈(n-1) m+2/3⌉ for m≥3 forand odd number m.
Corry Corazon Marzuki, Fitri Aryani, Rado Yendra and Ahmad Fudholi, 2018. Total Vertex Irregularity Strength of Comb Product Graph of Pm and Cn. Research Journal of Applied Sciences, 13: 83-86.