Domination polynomials of k-tree related graphs

S. Jahari; S. Alikhani

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arXiv · 1407.5959

Domination polynomials of k-tree related graphs

S. Jahari·S. Alikhani

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Abstract

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=\sum_{i=γ(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $γ(G)$ is the domination number of $G$. In this paper we study the domination polynomials of several classes of $k$-tree related graphs. Also, we present families of these kind of graphs, whose domination polynomial have no nonzero real roots.

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S. Jahari, S. Alikhani. 2014-07-22. Domination polynomials of k-tree related graphs. https://arxiv.org/abs/1407.5959

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