Recognisability of the sporadic groups by the isomorphism types of their prime graphs

Abstract The prime graph , also called the Gruenberg–Kegel graph , of a finite group 𝐺 is the labelled graph <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi mathvariant="normal">Γ</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> \Gamma(G) with vertices the prime divisors of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">|</m:mo> <m:mi>G</m:mi> <m