Bulletin of the Korean Mathematical Society , ( ISI ), Volume (53), No (4), Year (2016-10) , Pages (1017-1031)

Title : ( Generalized cayley graph of upper triangular matrix rings )

Authors: M. Afkhami , seyed hossein hashemifar , Kazem Khashyarmanesh ,

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Let R be a commutative ring with the non-zero identity and n be a natural number. T^n R is a simple graph with R^n \ {0} as the vertex set and two distinct vertices X and Y in R^n are adjacent if and only if there exists an n × n lower triangular matrix A over R whose entries on the main diagonal are non-zero such that AX^t = Y t or AY^ t = Xt, where, for a matrix B, B^t is the matrix transpose of B. T^n R is a generalization of Cayley graph. Let T^n(R) denote the n × n upper triangular matrix ring over R. In this paper, for an arbitrary ring R, we investigate the properties of the graph T^n_{T^n(R)}.

Keywords

, Cayley graph, matrix
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@article{paperid:1060925,
author = {M. Afkhami and Hashemifar, Seyed Hossein and Khashyarmanesh, Kazem},
title = {Generalized cayley graph of upper triangular matrix rings},
journal = {Bulletin of the Korean Mathematical Society },
year = {2016},
volume = {53},
number = {4},
month = {October},
issn = {1015-8634},
pages = {1017--1031},
numpages = {14},
keywords = {Cayley graph; matrix ring.},
}

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%0 Journal Article
%T Generalized cayley graph of upper triangular matrix rings
%A M. Afkhami
%A Hashemifar, Seyed Hossein
%A Khashyarmanesh, Kazem
%J Bulletin of the Korean Mathematical Society
%@ 1015-8634
%D 2016

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