Order divisor graphs of  finite groups

T. Chalapathi a and R. V M S S Kiran Kumar b,∗

Order divisor graphs of finite groups

Authors :

T. Chalapathi^a and R. V M S S Kiran Kumar ^b,∗

Author Address :

^a Department of Mathematics, Sree Vidyanikethan Engineering College, Tirupati-517502, Andhra Pradesh, India.
^b Department of Mathematics, S. V. University, Tirupati-517502, Andhra Pradesh, India.

*Corresponding author.

Abstract :

For each finite group $G$ we associate a simple undirected graph $OD(G)$, order divisor graph. We investigate the interconnection between the group theoretic properties of $G$ and the graph theoretic properties of order divisor graph $OD(G)$. For a finite group $G$, we obtain the density, the girth and the diameter of $OD(G)$. Further, we obtain the relation $Gcong G^prime$ if and only if $OD(G)cong OD(G^prime)$, for every distinct finite groups $G$ and $G^prime$, and $Auto(G)subseteq Auto(OD(G))$.

Keywords :

Finite group, finite subgroups, isomorphism, automorphism, order divisor graph.

DOI :

Article Info :

Received : January 17, 2017; Accepted : April 29, 2017.