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 t d i s ( 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.