Total distance vertex irregularity strength of some corona product graphs

Abstract

A distance vertex irregular total k-labeling of a simple undirected graph G = G(V, E), is a function f : V (G) ∪ E(G) −→ {1, 2, . . . , k} such that for every pair vertices u, v ∈ V (G) and u ̸ = v, the weights of u and v are distinct. The weight of vertex v ∈ V (G) is defined to be the sum of the label of vertices in neighborhood of v and the label of all incident edges to v. The total distance vertex irregularity strength of G (denoted by tdis(G)) is the minimum of k for which G has a distance vertex irregular total k-labeling. In this paper, we present several results of the total distance vertex irregularity strength of some corona product graphs.