TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS
محل انتشار: مجله ساختارهای جبری، دوره: 5، شماره: 2
سال انتشار: 1397
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 285
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شناسه ملی سند علمی:
JR_JAS-5-2_004
تاریخ نمایه سازی: 18 تیر 1398
چکیده مقاله:
Let $G = (V, E)$ 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 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 $G$. 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.
کلیدواژه ها:
نویسندگان
S. Alikhani
Department of Mathematics, Yazd University, ۸۹۱۹۵-۷۴۱, Yazd, Iran.
N. Jafari
Department of Mathematics, Yazd University, ۸۹۱۹۵-۷۴۱ Yazd, Iran.