Equal-Square Graphs Associated with Finite Groups

Abstract

The graphical representation of finite groups is studied in this paper. For each finite group, a simple graph is associated for which the vertex set contains elements of group such that two distinct vertices x and y are adjacent iff x2=y2. We call this graph an equal-square graph of the finite group G, symbolized by ESG. Some interesting properties of ESG are studied. Moreover, examples of equal-square graphs of finite cyclic groups, groups of plane symmetries of regular polygons, group of units Un, and the finite abelian groups are constructed.