Simple groups with m-regular first prime graph component

Authors : M Foroudi Ghasemabadi, A Iranmanesh

Pages : 705-716

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Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :Let G be a finite simple group and GKinsert ignore into journalissuearticles values(G); be the prime graph of G. The connected component of GKinsert ignore into journalissuearticles values(G); whose vertex set contains 2 is denoted by $\pi_1insert ignore into journalissuearticles values(G);$. In this paper, our purpose is to classify the finite simple groups G such that $\pi_1insert ignore into journalissuearticles values(G);$ is regular. We prove that $\pi_1insert ignore into journalissuearticles values(G);$ is regular if and only if all the connected components of GKinsert ignore into journalissuearticles values(G); are cliques.
Keywords : Prime graph, simple groups, regular graph