TOTAL DOMINATION POLYNOMIAL OF GRAPHS FROM PRIMARY SUBGRAPHS | ||
| Journal of Algebraic Systems | ||
| مقاله 4، دوره 5، شماره 2، فروردین 2018، صفحه 127-138 اصل مقاله (311.53 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2018.1096 | ||
| نویسندگان | ||
| S. Alikhani* 1؛ N. Jafari2 | ||
| 1Department of Mathematics, Yazd University, 89195-741, Yazd, Iran. | ||
| 2Department of Mathematics, Yazd University, 89195-741 Yazd, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Total domination number؛ total domination polynomial؛ total dominating set | ||
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آمار تعداد مشاهده مقاله: 703 تعداد دریافت فایل اصل مقاله: 1,119 |
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