This is the first full-length book on the major theme of symmetry in graphs. Forming part of
algebraic graph theory, this fast-growing field is concerned with the study of highly …

Let A be an abelian group and let ι be the automorphism of A defined by: ι: a↦ a− 1. A
Cayley graph Γ= Cay (A, S) is said to have an automorphism group as small as possible if …

It is well known that almost all graphs are canonizable by a simple combinatorial routine
known as color refinement. With high probability, this method assigns a unique label to each …

A Frobenius group is a transitive permutation group that is not regular and such that only the
identity fixes more than one point. A graphical Frobenius representation (GFR) of a …

It has long been known that a vertex-transitive graph $\Gamma $ is isomorphic to a double
coset graph $\text {Cos}(G, H, S) $ of a transitive group $ G\le\text {Aut}(\Gamma) $, a vertex …

The canonical double cover B (X) of a graph X is the direct product of X and K 2. If Aut (B
(X))≅ Aut (X)× Z 2 then X is called stable; otherwise X is called unstable. An unstable graph …

A canonical double cover B (X) of a graph X is the direct product of X and the complete
graph K 2 on two vertices. In order to answer the question when a canonical double cover of …

When dealing with symmetry properties of mathematical objects, one of the fundamental
questions is to determine their full automorphism group. In this paper this question is …

In this note, we introduce the notions of color-permutable automorphisms and color-
permutable vertex-transitive Cayley graphs of semigroups. As a main result, for a finite …

Abstract A Cayley digraph Cay (G, S) of a finite group G with respect to a subset S of G,
where S does not contain the identity 1 of G, is said to be a CI-digraph, if Cay (G, S)≅ Cay …