Caucal, Didier

We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.

Chen, Jiyong Jin, Wei Li, Cai Heng
Published in
Journal of Algebraic Combinatorics

A complete classification is given of 2-distance-transitive circulants, which shows that a 2-distance-transitive circulant is a cycle, a Paley graph of prime order, a regular complete multipartite graph, or a regular complete bipartite graph of order twice an odd integer minus a 1-factor.

Grimmett, Geoffrey R. Li, Zhongyang

Abstract: We study the connective constants of weighted self-avoiding walks (SAWs) on infinite graphs and groups. The main focus is upon weighted SAWs on finitely generated, virtually indicable groups. Such groups possess so-called height functions, and this permits the study of SAWs with the special property of being bridges. The group structure i...

Badaoui, Mohamad

Applying algebraic and combinatorics techniques to solve graph problems leads to the birthof algebraic and combinatorial graph theory. This thesis deals mainly with a crossroads questbetween the two theories, that is, the problem of constructing infinite families of expandergraphs.From a combinatorial point of view, expander graphs are sparse graph...

Doyle, John Kevin Tucker, Thomas W. Watkins, Mark E.
Published in
Journal of Algebraic Combinatorics

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 Frobenius group G is a graph whose automorphism group, as a group of permutations of the vertex set, is isomorphic to G. The problem of classifying which Frobenius groups ...

Kovács, István Kuzman, Boštjan Malnič, Aleksander Wilson, Stephen

Bicirkulant je graf, ki dopušča avtomorfizem z natanko dvema orbitama vozlišč enake velikosti. V članku so karakterizirani vsi neizomorfni 4-valentni povezavno tranzitivni bicirkulanti. Posledično je izpeljana karakterizacija 4-valentnih ločno tranzitivnih dihedrantov.

Nerad, Luka

Pušnik, Primož

Dobson, Edward Hujdurović, Ademir Kutnar, Klavdija Morris, Joy
Published in
Journal of Algebraic Combinatorics

An automorphism α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} of a Cayley graph Cay(G,S)\documentclass[12pt]{minimal} \usepackage{amsmath} \u...

Miklavič, Štefko Šparl, Primož

In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph ▫$Gamma$▫ is ▫$n$▫-HC-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton cycle of ▫$Gamma$▫. Similarly, ▫$Gamma$▫ is weakly ▫$n$▫-HP-extendable if it contains a path of length ▫$...