Shahrood University of TechnologyJournal of Algebraic Systems2345-51285220180101TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS127138109610.22044/jas.2018.1096ENS. AlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, Iran.N. JafariDepartment of Mathematics, Yazd University, 89195-741 Yazd, Iran.Journal Article20160925Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum d_t(G,i)$, where $d_t(G,i)$ is the number of total dominating sets of $G$ of size $i$. Let $G$ be a connected graph constructed from pairwise disjoint connected graphs $G_1,ldots ,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identify these two<br /> vertices. Then continue in this manner inductively. We say that $G$ is obtained by point-attaching from $G_1, ldots ,G_k$ and that $G_i$'s are the primary subgraphs of $G$. <br /> In this paper, we consider some particular cases of these graphs that most of them are of importance in chemistry and study their total domination polynomials.http://jas.shahroodut.ac.ir/article_1096_6bc97a7ad506ba2ec801a8f784bf5401.pdf