On the number of connected components of divisibility graph for certain simple groups

The divisibility graph \mathscr{D}(G) for a finite group G is a graph with vertex set cs(G)\setminus\{۱\}‎ ‎where cs(G) is the set of conjugacy class sizes of G‎. ‎Two vertices a and b are adjacent whenever a divides‎ ‎b or b divides a‎. ‎In this paper we will find the number of connected components of \mathscr{D}(G) where G is a‎ ‎simple Zassenhaus group or an sporadic simple group‎.

کلیدواژه ها:

‎Divisibility graph‎ ، ‎connected component‎ ، ‎Simple groups