Permutation groups are one of the oldest topics in algebra. Their study has recently been
revolutionized by new developments, particularly the Classification of Finite Simple Groups …

Abstract A $(k, g) $-cage is a $ k $-regular graph of girth $ g $ of minimum order. In this
survey, we present the results of over 50 years of searches for cages. We present the …

The endomorphism monoids of graphs have been actively investigated. They are
convenient tools expressing asymmetries of the graphs. One of the most important classes of …

The isomorphism problem for Cayley graphs has been extensively investigated over the
past 30 years. Recently, substantial progress has been made on the study of this problem …

On transitive Cayley graphs of groups and semigroups - ScienceDirect Skip to main contentSkip
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The Finite Primitive Permutation Groups Containing an Abelian Regular Subgroup Page 1
THE FINITE PRIMITIVE PERMUTATION GROUPS CONTAINING AN ABELIAN REGULAR …

For a positive integer s, a graph Γ is called s-arc transitive if its full automorphism group AutΓ
acts transitively on the set of s-arcs of Γ. Given a group G and a subset S of G with S= S− 1 …

Regular covers of complete graphs which are 2-arc-transitive are investigated. A
classification is given of all such graphs whose group of covering transformations is either …

A complete classification is given for finite vertex-primitive and vertex-biprimitive $ s $-
transitive graphs for $ s\ge 4$. The classification involves the construction of new 4-transitive …

A complete classification of 2-arc-transitive dihedrants, that is, Cayley graphs of dihedral
groups is given, thus completing the study of these graphs initiated by the third author in [D …