An atlas of domination polynomials of graphs of order at most six

Abstract

The domination polynomial of a graph $G$ of order $n$ 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 $G$. The roots of domination polynomial is called domination roots. In this article, we compute the domination polynomial and domination roots of all graphs of order less than or equal to 6, and show them in the tables.

arXiv commentThis atlas has published in the PhD thesis of the first author in 2009 and also in book "Dominating sets and domination polynomials of graphs: Domination polynomial: A new graph polynomial", LAMBERT Academic Publishing, ISBN: 9783847344827 (2012). Thanks to ArXiv for letting us to publish it here for more access