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 …

We consider circulant graphs having p vertices, with p prime. To any such graph we
associate a certain number k, that we call type of the graph. We prove that for p≫ k the …

A circulant (di) graph is a (di) graph on n vertices that admits a cyclic automorphism of order
n. This paper provides a survey of the work that has been done on finding the automorphism …

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 paper concerns the automorphism groups of Cayley graphs over cyclic groups which
have a rational spectrum (rational circulant graphs for short). With the aid of the techniques …

We attempt to determine the structure of the automorphism group of a generic circulant
graph. We first show that almost all circulant graphs have automorphism groups as small as …

The integral circulant graph $ X_n (D) $ has the vertex set $ Z_n=\{0, 1,\ldots $, $ n {-} 1\} $
and vertices $ a $ and $ b $ are adjacent, if and only if $\gcd (a {-} b $, $ n)\in D $, where …

We characterize the automorphism groups of circulant digraphs whose connection sets are
relatively small, and of unit circulant digraphs. For each class, we either explicitly determine …

Automorphism groups of Cayley digraphs of Z Page 1 Automorphism groups of Cayley
digraphs of Z 3 p Edward Dobson Department of Mathematics and Statistics Mississippi State …

An automorphism α α of a Cayley graph Cay (G, S) Cay (G, S) of a group G with connection
set S is color-preserving if α (g, gs)=(h, hs) α (g, gs)=(h, hs) or (h, hs^-1)(h, hs-1) for every …