Kriloff, Cathy Lay, Terry
Published in
Discrete Mathematics

Generalizing a result of Conway, Sloane, and Wilkes (1989) for real reflection groups, we show the Cayley graph of an imprimitive complex reflection group with respect to standard generating reflections has a Hamiltonian cycle. This is consistent with the long-standing conjecture that for every finite group, G, and every set of generators, S, of G ...

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.

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.

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...