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کاربرد نوع شرط:
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Stability,bondage number,dominated chromatic number
- چکیده:
- چکیده انگلیسی: Let $G$ be a simple graph. The dominated coloring of $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $chi_{dom}(G)$. Stability (bondage number) of dominated chromatic number of $G$ is the minimum number of vertices (edges) of $G$ whose removal changes the dominated chromatic number of $G$. In this paper, we study the dominated chromatic number, dominated stability and dominated bondage number of certain graphs.
- انتشار مقاله: 03-07-1398
- نویسندگان: Saeid Alikhani,Mohammad Reza Piri
- مشاهده
- جایگاه : پژوهشی
- مجله: Transactions on Combinatorics
- نوع مقاله: Journal Article
- کلمات کلیدی: Zero forcing number,generalized Sierpi'{n}ski graph,Sierpi'{n}ski graph,path covering
- چکیده:
- چکیده انگلیسی: In this article we study the Zero forcing number of Generalized Sierpi'{n}ski graphs $S(G,t)$. More precisely, we obtain a general lower bound on the Zero forcing number of $S(G,t)$ and we show that this bound is tight. In particular, we consider the cases in which the base graph $G$ is a star, path, a cycle or a complete graph.
- انتشار مقاله: 27-09-1395
- نویسندگان: Ebrahim Vatandoost,Fatemeh Ramezani,Saeid Alikhani
- مشاهده
- جایگاه : پژوهشی
- مجله: Khayyam Journal of Mathematics
- نوع مقاله: Journal Article
- کلمات کلیدی: domination number,distinguishing index,distinguishing number
- چکیده:
- چکیده انگلیسی: The distinguishing number (index) of a graph $G$ is the least integer $d$
such that $G$ has a vertex labeling (edge labeling) with $d$ labels that is preserved only by the trivial automorphism. A set $S$ of vertices in $G$ is a dominating set of $G$ if every vertex of $V(G)setminus S$ is adjacent to some vertex in $S$. The minimum cardinality of a dominating set of $G$ is the domination number of $G$. In this paper, we obtain some upper bounds for the distinguishing number and the distinguishing index of a graph based on its domination number.- انتشار مقاله: 07-11-1397
- نویسندگان: Saeid Alikhani,Samaneh Soltani
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: distinguishing index,edge-colourings,upper bound
- چکیده:
- چکیده انگلیسی: The distinguishing index of a simple graph $G$, denoted by $D'(G)$, is the least number of labels in an edge labeling of $G$ not preserved by any non-trivial automorphism. We prove that for a connected graph $G$ with maximum degree $Delta$, if the minimum degree is at least two, then $ D'(G)leq lceil sqrt{Delta }rceil +1$. We also present graphs $G$ for which $D'(G)leq lceil sqrt{Delta (G)}rceil$.
- انتشار مقاله: 12-09-1398
- نویسندگان: Saeid Alikhani,Samaneh Soltani
- مشاهده
- جایگاه : پژوهشی
- مجله: Algebraic Structures and Their Applications
- نوع مقاله: Journal Article
- کلمات کلیدی: Independent set,Independence number,Zero-divisor graph, Ideal
- چکیده:
- چکیده انگلیسی: Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ is
independent set of $G$, if no two vertices of $S$ are adjacent.
The independence number $alpha(G)$ is the size of a maximum
independent set in the graph.
In this paper we study and characterize the independent sets of
the zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph
$Gamma_I(R)$
of a commutative ring $R$.- انتشار مقاله: 03-05-1393
- نویسندگان: Saeid Alikhani,Saeed Mirvakili
- مشاهده