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

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 P2 and an arbitrary regular graph G.