Journal of the Australian Mathematical Society, ( ISI ), Volume (96), No (1), Year (2014-8) , Pages (289-302)

Title : ( Cayley sum graph of ideals of a commutative ring )

Authors: Mojgan Afkhami , Zahra Barati , Kazem Khashyarmanesh , nahid paknejad ,

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Let R be a commutative ring, I(R) be the set of all ideals of R and S be a subset of I^*(R) = I(R) -{0} We define a Cayley sum digraph of ideals of R, denoted by Cay^+(I(R),S) as a directed graph whose vertex set is the set I(R) and, for every two distinct vertices I and J, there is an arc from I to J, whenever I + K = J, for some ideal K in S . Also, the Cayley sum graph Cay^+(I(R); S ) is an undirected graph whose vertex set is the set I(R) and two distinct vertices I and J are adjacent whenever I + K = J or J + K = I, for some ideal K in S . In this paper, we study some basic properties of the graphs Cay^-(I(R); S ) and Cay^+(I(R); S ) such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of Cay^+(I(R); S ) and also we provide some characterization for rings R whose Cayley sum graphs have genus one.

Keywords

, Cayley sum graph, planar graph, clique number, genus
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@article{paperid:1046571,
author = {Mojgan Afkhami and Zahra Barati and Khashyarmanesh, Kazem and Paknejad, Nahid},
title = {Cayley sum graph of ideals of a commutative ring},
journal = {Journal of the Australian Mathematical Society},
year = {2014},
volume = {96},
number = {1},
month = {August},
issn = {1446-7887},
pages = {289--302},
numpages = {13},
keywords = {Cayley sum graph; planar graph; clique number; genus number},
}

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%0 Journal Article
%T Cayley sum graph of ideals of a commutative ring
%A Mojgan Afkhami
%A Zahra Barati
%A Khashyarmanesh, Kazem
%A Paknejad, Nahid
%J Journal of the Australian Mathematical Society
%@ 1446-7887
%D 2014

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