Highly total prime labeling for some duplicate graph

Abstract

Let G = (V, E) be a graph with p vertices and q edges. A bijection f : V ∪E → {1, 2, · · · , p+q} is said to be a highly total prime labeling if (i) for each edge e = uv, the labels assigned to u and v are relatively prime (ii) any pair of adjacent edges receives relatively prime labeling. A graph which admits highly total prime labeling is called highly total prime graph. In this paper we investigate the existence of highly total prime labeling of some duplicate graphs related to path Pn, cycle Cn and star Sn.