An Upper Bound On the Total Vertex Irregularity Strength of the Cartesian Product of P2 and an Arbitrary Regular Graph

Abstract

Abstract Let G be a connected and simple graph with vertex set V ( G ) and edge set E ( G ). A total labeling f : V ∪ E → {1, 2,. . ., k }is called a vertex irregular total k-labeling of G if every two distinct vertices x and y in V ( G ) satisfy wf ( x ) ≠ wf ( y ), where . The total vertex irregularity strength of G , denoted by tvs ( G ), is the minimum k for which G has a vertex irregular total k -labeling. In this paper, we provide an upper bound on the total vertex irregularity strength of the Cartesian product of P 2 and an arbitrary regular graph G .