Total vertex irregularity strength of wheel related graphs

Abstract

For a simple graph G with vertex set V (G) and edge set E(G), a labeling φ : V (G) ∪ E(G) → {1, 2, . . . , k} is called a vertex irregular total klabeling of G if for any two different vertices x and y, their weights wt(x) and wt(y) are distinct. The weight wt(x) of a vertex x in G is the sum of its label and the labels of all edges incident with the given vertex x. The total vertex irregularity strength of G, denoted by tvs(G), is the smallest positive integer k for which G has a vertex irregular total k-labeling. In this paper, we study the total vertex irregularity strength of flower, helm, generalized friendship and web graphs.