# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# Graphs with few domination roots

Presented by Dr. Saeid ALIKHANI
Type: Oral presentation
Track: General session

## Content

The domination polynomial of a graph $G$ of order $n$ is the polynomial $D(G,x)=\sum_{i=1}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating vertex sets of $G$ with cardinality $i$. A root of $D(G,x)$ is called a domination root of $G$. In this talk, we characterize graphs with at most four distinct domination roots. Finally we state some conjectures and open problems.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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