On the diameters of McKay graphs for finite simple groups

On finite simple groups and Kneser graphs

For a finite group G let (G) be the (simple) graph defined on the elements of G with an edge between two (distinct) vertices if and only if they generate G. The chromatic number of (G) is considered for various non-solvable groups G.

On Laplacian energy of non-commuting graphs of finite groups

‎Let $G$ be a finite non-abelian group with center $Z(G)$‎. ‎The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $Gsetminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy ne yx$‎. ‎In this paper‎, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups‎..

New refinements of the McKay conjecture for arbitrary finite groups

Let G be an arbitrary finite group and fix a prime number p. The McKay conjecture asserts that G and the normalizer in G of a Sylow p-subgroup have equal numbers of irreducible characters with degrees not divisible by p. The Alperin-McKay conjecture is version of this as applied to individual Brauer p-blocks of G. We offer evidence that perhaps much stronger forms of both of these conjectures a...

Distance Transitive Graphs and Finite Simple Groups

This paper represents the first step in the classification of finite primitive distance transitive graphs. In it we reduce the problem to the case where the automorphism group is either almost simple or affine. Let ^ be a simple, connected, undirected graph with vertex set Q. If oc, /? e Q, then d(a, j8) denotes the distance between a and /3 in §. Let G be some group of automorphisms of §. Then...

Expander Graphs and Finite Simple Groups