Dominating Sets and Domination Polynomials of Square of Paths
نویسندگان
چکیده
Let G = (V, E) be a simple graph. A set S V is a dominating set of G, if every vertex in V-S is adjacent to at least one vertex in S. Let be the square of the Path and let 2 n P n P 2 , n D P i denote the family of all dominating sets of with cardinality i. Let 2 n P 2 , n n d P i D P i 2 , . In this paper, we obtain a recursive formula for . Using this recursive formula, we construct the polynomial, 2 , n d P i 2 5 , n 2 , n i n n i x d P i x D P , which we call domination polynomial of and obtain some properties of this polynomial. 2 n P
منابع مشابه
Some Families of Graphs whose Domination Polynomials are Unimodal
Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal.
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