Permutation groups, their fundamental theory and applications are discussed in this
introductory book. It focuses on those groups that are most useful for studying symmetric …

This paper provides new observations on the Lovász θ-function of graphs. These include a
simple closed-form expression of that function for all strongly regular graphs, together with …

This book gives a proof of Cherlin's conjecture for finite binary primitive permutation groups.
Motivated by the part of model theory concerned with Lachlan's theory of finite …

Let R be a commutative ring with unity and R+, U (R), and Z*(R) be the additive group, the
set of unit elements, and the set of all nonzero zero-divisors of R, respectively. We denote by …

Let OG (4) denote the family of all graph-group pairs (Γ, G) where Γ is finite, 4-valent,
connected, and G-oriented (G-half-arc-transitive). A subfamily of OG (4) has recently been …

We investigate the family of vertex-transitive graphs with diameter 2. Let Γ be such a graph.
Suppose that its automorphism group is transitive on the set of ordered non-adjacent vertex …

Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups Page 1 Lecture Notes in
Mathematics 2302 Nick Gill Martin W. Liebeck Pablo Spiga Cherlin’s Conjecture for Finite …

In this paper, we first investigate the family of vertex-transitive diameter 2 hexavalent graphs
and particularly completely determine such graphs whose automorphism group is transitive …

We examine the class of G-arc-transitive graphs with at least one nontrivial complete normal
quotient, such that all other normal quotients are either complete or empty graphs. Such …

Let OG (4) denote the family of all graph-group pairs (Γ, G) where Γ is 4-valent, connected
and G-oriented (G-half-arc-transitive). Using a novel application of the structure theorem for …