Recognition of Janko groups and some simple $K_4$-groups by the order and one irreducible character degree or character degree graph

Abstract

‎In this paper we prove that some Janko groups are uniquely‎ ‎determined by their orders and one irreducible character‎ ‎degree‎. ‎Also we prove that some finite simple $K_4$-groups are‎ ‎uniquely determined by their character degree graphs and their‎ ‎orders‎.