Feng, Yan-Quan Kutnar, Klavdija Marusic, Dragan Zhang, Cui

A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper tetravalent one-regular graphs of order 4p^{2}, where p is a prime, are classified.

Feng, Yan-Quan Kutnar, Klavdija Marusic, Dragan Zhang, Cui

A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper tetravalent one-regular graphs of order 4p^{2}, where p is a prime, are classified.

Dobson, Edward Morris, Joy
Published in
Graphs and Combinatorics

We show that a quotient group of a CI-group with respect to (di)graphs is a CI-group with respect to (di)graphs.

Bamberg, John Gill, Nick Hayes, Thomas P. Helfgott, Harald A. Seress, Ákos Spiga, Pablo
Published in
Journal of Algebraic Combinatorics

In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\operatorname...

Vetrík, Tomáš
Published in
Graphs and Combinatorics

Let CCd,k be the largest possible number of vertices in a cyclic Cayley graph of degree d and diameter k, and let ACd,k be the largest order in an Abelian Cayley graph for given d and k. We show that CCd,2≥1336(d+2)(d-4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{ams...

Devillers, Alice Jin, Wei Li, Cai Heng Praeger, Cheryl E.
Published in
Journal of Algebraic Combinatorics

We investigate connected normal 2-geodesic transitive Cayley graphs Cay(T,S). We first prove that if Cay(T,S) is neither cyclic nor K4[2], then 〈a〉∖{1}⊆̷S for all a∈S. Next, as an application, we give a reduction theorem proving that each graph in this family which is neither a complete multipartite graph nor a bipartite 2-arc transitive graph, has...

Alaeiyan, Mehdi Mirzajani, Javad
Published in
Mathematical Sciences

For a group G, and a subset S of G such that 1G ∉ S, let X = Cay(G,S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal.AM...

Kovács, István Marušič, Dragan Muzychuk, Mikhail
Published in
Journal of Algebraic Combinatorics

A graph Γ is said to be G-arc-regular if a subgroup \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G \le\operatorname{\mathsf{Aut}}(\varGamma)$\end{document} acts regul...

Exoo, Geoffrey Jajcay, Robert Širáň, Jozef
Published in
Journal of Algebraic Combinatorics

A (k,g)-Cayley cage is a k-regular Cayley graph of girth g and smallest possible order. We present an explicit construction of (k,g)-Cayley graphs for all parameters k≥2 and g≥3 and generalize this construction to show that many well-known small k-regular graphs of girth g can be constructed in this way. We also establish connections between this c...

Li, Xiangwen Mak-Hau, Vicky Zhou, Sanming
Published in
Journal of Combinatorial Optimization

A k-L(2,1)-labelling of a graph G is a mapping f:V(G)→{0,1,2,…,k} such that |f(u)−f(v)|≥2 if uv∈E(G) and f(u)≠f(v) if u,v are distance two apart. The smallest positive integer k such that G admits a k-L(2,1)-labelling is called the λ-number of G. In this paper we study this quantity for cubic Cayley graphs (other than the prism graphs) on dihedral ...