Simple groups with m-regular first prime graph component

Abstract

Let G be a finite simple group and GK(G) be the prime graph of G. The

connected component of GK(G) whose vertex set contains 2 is denoted

by $\pi_1(G)$. In this paper, our purpose is to classify the finite simple

groups G such that $\pi_1(G)$ is regular. We prove that $\pi_1(G)$ is regular if

and only if all the connected components of GK(G) are cliques.

Keywords

• Prime graph,simple groups,regular graph

References

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