On the domination polynomials of non P4-free graphs

Author(s):

Saeid Alikhani

Message:
Abstract:
A graph $G$ is called $P_4$-free, if $G$ does not contain an induced subgraph $P_4$. 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 sets of $G$ of size $i$. Every root of $D(G,x)$ is called a domination root of $G$. In this paper we state and prove formula for the domination polynomial of non $P_4$-free graphs. Also, we pose a conjecture about domination roots of these kind of graphs.
Keywords:

Domination polynomial , Simple path , Root

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:8 Issue: 2, Nov 2013
Pages:
45 to 55
https://www.magiran.com/p1186122  
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