Volume 8, Issue 2 (10-2013)                   IJMSI 2013, 8(2): 49-55 | Back to browse issues page

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Alikhani S. On the domination polynomials of non P4-free graphs. IJMSI. 2013; 8 (2) :49-55
URL: http://ijmsi.ir/article-1-504-en.html

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.

Type of Study: Research paper | Subject: General

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