On total irregularity strength of star graphs, double-stars and caterpillar
Diari Indriati, Widodo Widodo, Indah Emilia Wijayanti, Kiki Ariyanti Sugeng · AIP conference proceedings · 2016
For a simple graph G = (V, E) with the vertex set V and the edge set E, a totally irregular total k-labeling f : V ∪ E → {1, 2,…, k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x′, their weights wt f(x) = f(x) + ∑xy∈E f (xy) and wtf (x′) = f (x′) + ∑x′ y′ ∈E f (x′y′) are distinct, and for any two different edges xy and x′y′ their weights f (x) + f (xy) + f (y) and f (x′) + f (x′y′) + f (y′) are also distinct. A total irregularity strength of graph G, denoted by ts(G), is defined as the minimum k for which G has a totally irregular total k-labeling. In this paper, we determine the exact value of the total irregularity strength for star graphs, double stars and caterpillar.