@article{article_524347, title={Simple groups with m-regular first prime graph component}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={45}, pages={705–716}, year={2016}, author={Ghasemabadi, M. Foroudi and Iranmanesh, A.}, keywords={Prime graph,simple groups,regular graph}, abstract={<div>Let G be a finite simple group and GK(G) be the prime graph of G. The </div> <div>connected component of GK(G) whose vertex set contains 2 is denoted </div> <div>by $\pi_1(G)$. In this paper, our purpose is to classify the finite simple </div> <div>groups G such that $\pi_1(G)$ is regular. We prove that $\pi_1(G)$ is regular if </div> <div>and only if all the connected components of GK(G) are cliques. </div>}, number={3}, publisher={Hacettepe University}