On Distance Vertex Irregular Total k-Labeling

Abstract

Let H= (T,S), be a finite simple graph, T(H)= T and S(H)= S, respectively, are the sets of vertices and edges on H. Let sigama:T∪S→1,2,• • •,k, be a total k-labeling on H and wsigama (x), be a weight of xT while using sigama labeling, which is evaluated based on the total number of all vertices labels in the neighborhood x and its incident edges. If every xT has a different weight, then sigama is a distance vertex irregular total k-labeling (DVITL). Total distance vertex irregularity strength of H (tdis(H) is defined as the least k for which H has a DVITL. Our research investigates the DVITL of the path (Pr) and cycle (Cr) graphs. We establish a lower bound and then calculate the precise value of tdis(Pr) and tdis(Cr).