Schlage-Puchta, Jan-Christoph
Published in
Combinatorica

Let π,σ ∈ Sn be chosen at random. Using character estimates we show that in various aspects the elements πσi behave like independent random variables. As application we show that almost surely the Cayley graph determined by π and σ has diameter O(n3 logn), and the directed Cayley-graph has almost surely diameter O(n4 logn). Further we describe an a...

Kovács, István
Published in
Graphs and Combinatorics

Let G be a finite group with identity element 1, and S be a subset of G such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1 \notin S}$$\end{document} and S = S...

Zhu, Yongwen
Published in
Semigroup Forum

Following Zhu (Semigroup Forum, 2011, doi:10.1007/s00233-011-9368-9), we study generalized Cayley graphs of semigroups. The Cayley D-saturated property, a particular combinatorial property, of generalized Cayley graphs of semigroups is considered and most of the results in Kelarev and Quinn (Semigroup Forum 66:89–96, 2003), Yang and Gao (Semigroup ...

Zhang, Zhen Xiao, Wenjun
Published in
Cluster Computing

This paper introduces a new type of Cayley graphs for building large-scale interconnection networks, namely \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathit{WG}_{...

Conder, Marston D. E. Feng, Yan-Quan
Published in
Journal of Algebraic Combinatorics

A graph is arc-regular if its automorphism group acts sharply-transitively on the set of its ordered edges. This paper answers an open question about the existence of arc-regular 3-valent graphs of order 4m where m is an odd integer. Using the Gorenstein–Walter theorem, it is shown that any such graph must be a normal cover of a base graph, where t...

Song, Shu-Jiao Li, Cai Heng Wang, Dianjun
Published in
Journal of Algebraic Combinatorics

A characterization is given of the class of edge-transitive Cayley graphs of Frobenius groups \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{Z}_{p^{d}}{:}\mathb...

Li, Lan Xiao, Wenjun
Published in
Frontiers of Computer Science in China

Many structured peer-to-peer (P2P) systems supported by distributed hash table (DHT) schemas have been proposed recently to improve the scalability of distributed virtual application systems. By organizing the peers based on interconnection topologies, existing proposed schemas are purely based on the logical relationship without knowledge of the p...

Feng, YQ Kwak, JH Wang, XY Zhou, JX

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Somlai, Gábor
Published in
Journal of Algebraic Combinatorics

For every prime p>2 we exhibit a Cayley graph on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{Z}_{p}^{2p+3}$\end{document} which is not a CI-graph. This prove...

Palcoux, Sébastien

Using unusual objects in the theory of von Neumann algebra, as the chinese game Go or the Conway game of life (generalized on finitely presented groups), we are able to build, by hands, many type III factors.