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

Abstract

The divisibility graph D(G) D(G) for a finite group G G is a graph with vertex set cs(G)∖{1} cs(G)∖{1}‎ ‎where cs(G) cs(G) is the set of conjugacy class sizes of G G‎. ‎Two vertices a a and b b are adjacent whenever a a divides‎ ‎b b or b b divides a a‎. ‎In this paper we will find the number of connected components of D(G) D(G) where G G is a‎ ‎simple Zassenhaus group or an sporadic simple group‎.

Keywords

• ‎Divisibility graph‎
• ‎Connected component‎
• ‎Simple groups