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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Independence number,domination number,Comaximal ideal graph,Genus of graph
- چکیده:
- چکیده انگلیسی: Let $R$ be a commutative ring with unity. The comaximal ideal graph of $R$, denoted by $mathcal{C}(R)$, is a graph whose vertices are the proper ideals of $R$ which are not contained in the Jacobson radical of $R$, and two vertices $I_1$ and $I_2$ are adjacent if and only if $I_1 +I_2 = R$. In this paper, we classify all comaximal ideal graphs with finite independence number and present a formula to calculate this number. Also, the domination number of $mathcal{C}(R)$ for a ring $R$ is determined. In the last section, we introduce all planar and toroidal comaximal ideal graphs. Moreover, the commutative rings with isomorphic comaximal ideal graphs are characterized. In particular we show that every finite comaximal ideal graph is isomorphic to some $mathcal{C}(mathbb{Z}_n)$.
- انتشار مقاله: 05-05-1394
- نویسندگان: Hamid Reza Dorbidi,Raoufeh Manaviyat
- مشاهده
- جایگاه : پژوهشی
- مجله: International Journal of Group Theory
- نوع مقاله: Journal Article
- کلمات کلیدی: Automorphism group,coprime graph,Planner graph
- چکیده:
- چکیده انگلیسی: In this paper we study the coprime graph of a group $G$. The coprime graph of a group $G$, denoted by $Gamma_G$, is a graph whose vertices are elements of $G$ and two distinct vertices $x$ and $y$ are adjacent if and only if $(|x|,|y|)=1$. In this paper, we show that $chi(Gamma_G)=omega(Gamma_G).$ We classify all the groups which $Gamma_G$ is a complete $r-$partite graph or a planar graph. Also we study the automorphism group of $Gamma_G$.
- انتشار مقاله: 09-08-1393
- نویسندگان: Hamid Reza Dorbidi,Hamid Reza Dorbidi,Hamid Reza Dorbidi
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Connected graph,Frobenius group,Order graph,Prime graph
- چکیده:
- چکیده انگلیسی: The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$.
In this paper, we study the connectivity and diameter of this graph. Also we give a relation between the order graph and prime graph of a group.- انتشار مقاله: 10-02-1394
- نویسندگان: Hamid Reza Dorbidi,Hamid Reza Dorbidi,Hamid Reza Dorbidi
- مشاهده