IMCS/Publications/CSJM/Issues/CSJM v.26, n.2 (77), 2018/

Invertible Graphs of Finite Groups

Authors: T. Chalapathi, R.V.M.S.S. Kiran Kumar
Keywords: Self-inverse elements, Mutual inverse elements, Weakly-perfect, Isomorphic graphs, Invertible graph.


We investigate some properties of invertible graphs of finite groups, which are newly defined in this paper. The main results have been proved using finite group classification. For each finite group, the size, the girth, the diameter, the clique number and the chromatic number have been studied. These studies show that the invertible graphs are weakly perfect. Specifically, formulas for enumerating a total number of edges in the invertible graph of the Symmetric group and Dihedral group have been derived. Further, the relations between isomorphic, non-isomorphic groups and their invertible graphs are presented.

T. Chalapathi
Department of Mathematics, Sree Vidyanikethan Eng. College,
Andhra Pradesh, India
Phone: +91 9542865332

R. V. M. S. S. Kiran Kumar,
Department of Mathematics, S.V. University,
Andhra Pradesh, India
Phone: +91 9493523133


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