Fuad, T. S. R. Phillips, J. D. Shen, Xiaorong
Published in
Southeast Asian Bulletin of Mathematics

The right universal multiplication group of a quandle in the variety of all quandles is constructable from the right Cayley graph of that quandle.

Haizhu, Li Jianfang, Wang Liang, Sun
Published in
Acta Mathematicae Applicatae Sinica

In this paper, it is proved that any connected Cayley graph on an abelian group of order pq orp2 has a hamiltonian decomposition, wherep andq are odd primes. This result answers partially a conjecture of Alspach concerning hamiltonian decomposition of 2k-regular connected Cayley graphs on abelian groups.

Shiying, Wang Yuren, Zhang Yan, Liu
Published in
Applied Mathematics-A Journal of Chinese Universities

Let Sn be the symmetric group, gi+=(123i), gi−=(li32) and Mn+={gi+∶4≤i≤n}, then Mn+ is a minimal generating set of Sn, where n≥5. It is proved that Cayley graph Cay (Sn, Mn+∩Mn−) is Hamiltonian and edge symmetric.

Solomyak, Rita
Published in
Journal of Theoretical Probability

Let Γ be a Cayley graph of a finitely generated group G. Subgraphs which contain all vertices of Γ, have no cycles, and no finite connected components are called essential spanning forests. The set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathr...

Bertacchi, D. Zucca, F.
Published in
Journal of Statistical Physics

We study the equidistribution on spheres of the n-step transition probabilities of random walks on graphs. We give sufficient conditions for this property being satisfied and for the weaker property of asymptotical equidistribution. We analyze the asymptotical behaviour of the Green function of the simple random walk on ℤ2 and we provide a class of...

Li, Cai Heng
Published in
Journal of Algebraic Combinatorics

Latifi, Shahram Srimani, Pradip K.
Published in
The Journal of Supercomputing

We propose a family of regular Cayley network graphs of degree three based on permutation groups for design of massively parallel systems. These graphs are shown to be based on the shuffle exchange operations, to have logarithmic diameter in the number of vertices, and to be maximally fault tolerant. We investigate different algebraic properties of...

Wang, Changqun Wang, Dianjun Xu, Mingyao
Published in
Science in China Series A: Mathematics

LetG be a finite group and let S be a nonempty subset of G not containing the identity element 1. The Cayley (di) graph X = Cay(G, S) of G with respect to S is defined byV (X)=G, E (X)={(g,sg)|g∈G, s∈S} A Cayley (di) graph X = Cay (G,S) is said to be normal ifR(G) ◃A = Aut (X). A group G is said to have a normal Cayley (di) graph if G has a subset ...

Deserable, Dominique Centre National de la Recherche Scientif... Rennes-1 Univ., 35 (France). Inst. de Re... Institut National des Sciences Appliquee... Institut National de Recherche en Inform...

France

Deserable, Dominique Centre National de la Recherche Scientif... Rennes-1 Univ., 35 (France). Inst. de Re... Institut National des Sciences Appliquee... Institut National de Recherche en Inform...

France