Linear Algebra and its Applications, ( ISI ), Volume (437), No (1), Year (2012-5) , Pages (1040-1049)

Title : ( Generalized Cayley graphs associated to commutative rings )

Authors: M. Afkhami , Kazem Khashyarmanesh , khosro nafar ,

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Let R be a commutative ring with identity element. For a natural number n, we associate a simple graph, denoted by Gamma^n_R , with R^n setminus { as the vertex set and two distinct vertices X and Y in R^n being adjacent if and only if there exists an n times n lower triangular matrix A over R whose entries on the main diagonal are non-zero and such that AX^T=Y^Tor AY^T=X^T, where, for a matrix B, B^T is the matrix transpose of B. When we consider the ring R as a semigroup with respect to multiplication, then Gamma^1_R is the usual undirected Cayley graph (over a semigroup). Hence Gamma^n_R is a generalization of Cayley graph. In this paper we study some basic properties of Gamma^n_R. We also determine all isomorphic classes of finite commutative rings whose generalized Cayley graph has genus at most three.

Keywords

, Cayley graph, Genus, Planar graph, Toroidal
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@article{paperid:1028331,
author = {M. Afkhami and Khashyarmanesh, Kazem and Nafar, Khosro},
title = {Generalized Cayley graphs associated to commutative rings},
journal = {Linear Algebra and its Applications},
year = {2012},
volume = {437},
number = {1},
month = {May},
issn = {0024-3795},
pages = {1040--1049},
numpages = {9},
keywords = {Cayley graph; Genus; Planar graph; Toroidal graph},
}

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%0 Journal Article
%T Generalized Cayley graphs associated to commutative rings
%A M. Afkhami
%A Khashyarmanesh, Kazem
%A Nafar, Khosro
%J Linear Algebra and its Applications
%@ 0024-3795
%D 2012

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