TY - JOUR T1 - On the domination polynomials of non P4-free graphs TT - JF - IJMSI JO - IJMSI VL - 8 IS - 2 UR - http://ijmsi.ir/article-1-504-en.html Y1 - 2013 SP - 49 EP - 55 KW - Domination polynomial KW - Simple path KW - Root. N2 - 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. M3 10.7508/ijmsi.2013.02.005 ER -