Composite Graph of a Group

Chinmayee Kumar

Abstract: Let G be a finite group. The Composite graph ?(G) of G is a graph with vertices as the elements of G, and two vertices a and b are adjacent if either o(a)=o(b) or gcd?(o(a),o(b)) is a composite number. In this paper, we study the structure of ?(G) graphs, for some abelian and non-abelian groups. Further, we see that if two groups G_1 and G_2 are such that G_1?G_2, then ?(G_1)??(G_2).

Keywords: Composite graph, Cyclic group