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arXiv · 0908.3305

Cycles are determined by their domination polynomials

Saieed Akbari·Mohammad Reza Oboudi
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Abstract

Let $G$ be a simple graph of order $n$. A dominating set of $G$ is a set $S$ of vertices of $G$ so that every vertex of $G$ is either in $S$ or adjacent to a vertex in $S$. The domination polynomial of $G$ is the polynomial $D(G,x)=\sum_{i=1}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. In this paper we show that cycles are determined by their domination polynomials.

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Saieed Akbari, Mohammad Reza Oboudi. 2009-08-23. Cycles are determined by their domination polynomials. https://arxiv.org/abs/0908.3305

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