Total Prime Labeling of Some Graphs
S. Meena, A. Ezhil · International Journal of Research in Advent Technology · 2019
In this paper, we investigate the existence of prime labeling for some classes of graphs.Let G = (V,E) be a graph with "p" vertices and "q" edges.A labeling f: VUE {1,2,3,……,(p+q)} is said to admit total prime labeling if for each edge e = uv, the labels assigned to u and v are relative prime, and for each vertex of degree atleast two, the greatest common divisor of the labels on the incident edges is one.A graph which admits total prime labeling is called total prime graph.We prove that the graphs Wheel (W n ), Gear (G n ), Carona (C 4Ͼ K 5 ), Triangular book (B 3 n ), Splitting graph of a star (K 1,n ), Double comb and Planter graph (R n ) are all total prime graphs.