A bipartite graph associated to Hamiltonian degrees of finite groups

Abstract

In this article, we employ the notion of Hamiltonian degree to connect group theory with graph theory. To do this, we present a new graph associated with a finite group G represented by the symbol ΓP(G). We explore ΓP(G)’s structural characteristics, such as its connectedness, planarity, vertex degrees, regularity, and the characteristics of its generated subgraphs.

Keywords: Dihedral Group, Star Graph, Bipartite Graph, Regular Graph, Hamiltonian Degree