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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Vertex decomposable,shellabel,Cohen-Macaulay
- چکیده:
- چکیده انگلیسی: Let $G$ be a finite simple graph on the vertex set $V(G)$ and let $S subseteq V(G)$. Adding a whisker to $G$ at $x$ means adding a new vertex $y$ and edge $xy$ to $G$ where $x in V(G)$. The graph $Gcup W(S)$ is obtained from $G$ by adding a whisker to every vertex of $S$. We prove that if $Gsetminus S$ is either a graph with no chordless cycle of length other than $3$ or $5$, chordal graph or $C_5$, then $G cup W(S)$ is a vertex decomposable graph.
- انتشار مقاله: 03-09-1393
- نویسندگان: Nasser Hajisharifi,Abolfazl Tehranian
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Independence number,Clique number,Complete graph,Well-covered,Vertex decomposable
- چکیده:
- چکیده انگلیسی: Let $ mathbb {Z}_{n} $ be the ring of integers modulo $ n $. The unitary Cayley graph of $ mathbb {Z}_{n} $ is defined as the graph $ G( mathbb {Z}_{n} ) $ with the vertex set $ mathbb {Z}_{n} $ and two distinct vertices $a,b$ are adjacent if and only if $a-bin Uleft( mathbb {Z}_{n}right)$, where $ Uleft( mathbb {Z}_{n}right) $ is the set of units of $ mathbb {Z}_{n} $. Let $Gamma ( mathbb {Z}_{n} ) $ be the complement of $ G( mathbb {Z}_{n} ) $. In this paper, we determine the independence number of $ Gamma ( mathbb {Z}_{n} ) $. Also it is proved that $ Gamma ( mathbb {Z}_{n} ) $ is well-covered. Among other things, we provide condition under which $ Gamma ( mathbb {Z}_{n} ) $ is vertex decomposable.
- انتشار مقاله: 02-07-1397
- نویسندگان: Morteza Vafaei,Abolfazl Tehranian,Reza Nikandish
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: commutative rings,annihilating-ideal,principal ideal,graph
- چکیده:
- چکیده انگلیسی: Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where $mathbb{P}(R)$ is the set of proper principal ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=(0)$. Then, we study some basic properties of $mathbb{AG}_P(R)$. For instance, we characterize rings for which $mathbb{AG}_P(R)$ is finite graph, complete graph, bipartite graph or star graph. Also, we study diameter and girth of $mathbb{AG}_P(R)$. Finally, we compare the principal ideal subgraph $mathbb{AG}_P(R)$ and spectrum subgraph $mathbb{AG}_s(R)$.
- انتشار مقاله: 06-07-1394
- نویسندگان: Reza Taheri,Abolfazl Tehranian
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: total graph,domination number,Module
- چکیده:
- چکیده انگلیسی: Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ and
investigate the necessary conditions for being $mathbb{Z}_{n}$ as module over $mathbb{Z}_{m}$ and we find the domination number of $T(Gamma(mathbb{Z}_{n}))$.- انتشار مقاله: 16-12-1393
- نویسندگان: Abbas Shariatnia,Abolfazl Tehranian
- مشاهده