The central vertices and radius of the regular graph of ideals
The regular graph of ideals of the commutative ring $R$, denoted by ${Gamma_{reg}}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-reg...
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University of Isfahan
2017-12-01
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| Series: | Transactions on Combinatorics |
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| Online Access: | http://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf |
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doaj-c51241e6c7314769b7f364fc2fed5fcf2020-11-25T02:45:33ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652017-12-016411310.22108/toc.2017.2147221472The central vertices and radius of the regular graph of idealsFarzad Shaveisi0Razi UniversityThe regular graph of ideals of the commutative ring $R$, denoted by ${Gamma_{reg}}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is proved that the radius of $Gamma_{reg}(R)$ equals $3$. The central vertices of $Gamma_{reg}(R)$ are determined, too.http://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdfArcartinian ringeccentricityradiusregular digraph |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Farzad Shaveisi |
| spellingShingle |
Farzad Shaveisi The central vertices and radius of the regular graph of ideals Transactions on Combinatorics Arc artinian ring eccentricity radius regular digraph |
| author_facet |
Farzad Shaveisi |
| author_sort |
Farzad Shaveisi |
| title |
The central vertices and radius of the regular graph of ideals |
| title_short |
The central vertices and radius of the regular graph of ideals |
| title_full |
The central vertices and radius of the regular graph of ideals |
| title_fullStr |
The central vertices and radius of the regular graph of ideals |
| title_full_unstemmed |
The central vertices and radius of the regular graph of ideals |
| title_sort |
central vertices and radius of the regular graph of ideals |
| publisher |
University of Isfahan |
| series |
Transactions on Combinatorics |
| issn |
2251-8657 2251-8665 |
| publishDate |
2017-12-01 |
| description |
The regular graph of ideals of the commutative ring $R$, denoted by ${Gamma_{reg}}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is proved that the radius of $Gamma_{reg}(R)$ equals $3$. The central vertices of $Gamma_{reg}(R)$ are determined, too. |
| topic |
Arc artinian ring eccentricity radius regular digraph |
| url |
http://toc.ui.ac.ir/article_21472_57a7aea214c4516a524744b78f00943a.pdf |
| work_keys_str_mv |
AT farzadshaveisi thecentralverticesandradiusoftheregulargraphofideals AT farzadshaveisi centralverticesandradiusoftheregulargraphofideals |
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1724761944691310592 |