Total vertex irregularity strength of wheel related graphs.
Ali Hasan Ahmad, Khalid Mahmood Awan, Imran Javaid, Slamin Slamin · 2011
For a simple graph G with vertex set V (G) andedgesetE(G), a labeling φ: V (G) ∪ E(G) − → {1, 2,...,k} is called a vertex irregular total k-labeling 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.