P. Jeyanthi and A.Sudha, On the total irregularity strength of some graphs, Bulletin of the International Mathematical Virtual Institute, Vol.9(2)(2019), 393-401. (original) (raw)

A totally irregular total k-labeling f : V ∪ E → {1, 2, 3,. .. , k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and y their vertex-weights wt h (x) = wt h (y) where the vertex-weight wt h (x) = h(x) + xy∈E h(xz) and also for every two different edges xy and x ′ y ′ of G their edge-weights wt h (xy) = h(x) + h(xy) + h(y) and wt h (x ′ y ′) = h(x ′) + h(x ′ y ′) + h(y ′) are distinct. A total irregularity strength of graph G, denoted by ts(G) is defined as the minimum k for which a graph G has a totally irregular total k-labeling. In this paper, we investigate double fan, double triangular snake, joint-wheel and Pm + Km whose total irregularity strength equals to the lower bound. 2010 Mathematics Subject Classification. 05C78. Key words and phrases. vertex irregular total k-labeling; edge irregular total k-labeling; total irregularity strength;double fan graph;double triangular snake graph; joint-wheel graph.