On Total Vertex Irregularity Strength of Hypercubes - Anita Hadi, Dian
The concept of total vertex irregularity labelling was introduced by Ba?ca et al. (2007). Let G = (V;E) be a simple graph (without loop and multiple edges). A function : V [ E ! f1; 2; :::; kg is called a vertex-irregular total k????labelling of G if for any two different vertices u and v in V satisfy wt(u) 6= wt(v), where wt(u) = (u)+ P uw2E (uw): 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-labelling. Baca, et al. (2007) derived the lower and upper bounds for any r-regular graph G with p vertices and q edges as follows: p+r r+1