A graph associated to proper non-small ideals of a commutative ring
S. Ebrahimi Atani; S. Dolati Pish Hesari; M. Khoramdel
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 1, page 1-12
- ISSN: 0010-2628
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topAtani, S. Ebrahimi, Hesari, S. Dolati Pish, and Khoramdel, M.. "A graph associated to proper non-small ideals of a commutative ring." Commentationes Mathematicae Universitatis Carolinae 58.1 (2017): 1-12. <http://eudml.org/doc/287901>.
@article{Atani2017,
abstract = {In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring $R$, denoted by $G(R)$, is a graph with all non-small proper ideals of $R$ as vertices and two distinct vertices $I$ and $J$ are adjacent if and only if $I\cap J$ is not small in $R$. In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection graph as diameter, girth, clique number, cut vertex, planar property and independence number. Further, it is shown that the independence number of a small graph of a ring $R$ is equal to the number of its maximal ideals and the domination number of small graph is at most 2.},
author = {Atani, S. Ebrahimi, Hesari, S. Dolati Pish, Khoramdel, M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {small ideal; small intersection graph; clique number; independence number; domination number; planar property; semirings; prime strong co-ideals; primal strong co-ideals; subtractive strong co-ideals},
language = {eng},
number = {1},
pages = {1-12},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A graph associated to proper non-small ideals of a commutative ring},
url = {http://eudml.org/doc/287901},
volume = {58},
year = {2017},
}
TY - JOUR
AU - Atani, S. Ebrahimi
AU - Hesari, S. Dolati Pish
AU - Khoramdel, M.
TI - A graph associated to proper non-small ideals of a commutative ring
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 1
SP - 1
EP - 12
AB - In this paper, a new kind of graph on a commutative ring is introduced and investigated. Small intersection graph of a ring $R$, denoted by $G(R)$, is a graph with all non-small proper ideals of $R$ as vertices and two distinct vertices $I$ and $J$ are adjacent if and only if $I\cap J$ is not small in $R$. In this article, some interrelation between the graph theoretic properties of this graph and some algebraic properties of rings are studied. We investigated the basic properties of the small intersection graph as diameter, girth, clique number, cut vertex, planar property and independence number. Further, it is shown that the independence number of a small graph of a ring $R$ is equal to the number of its maximal ideals and the domination number of small graph is at most 2.
LA - eng
KW - small ideal; small intersection graph; clique number; independence number; domination number; planar property; semirings; prime strong co-ideals; primal strong co-ideals; subtractive strong co-ideals
UR - http://eudml.org/doc/287901
ER -
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