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On relation between the Kirchhoff index and number of spanning trees of graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 10، دوره 5، شماره 1، شهریور 2020، صفحه 1-8 اصل مقاله (392.02 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2019.26270.1088 | ||
| نویسندگان | ||
| Igor Milovanovic* 1؛ Edin Glogic2؛ Marjan Matejic3؛ Emina Milovanovic1 | ||
| 1Faculty of Electronic Engineering, Nis, Serbia | ||
| 2State University of Novi Pazar, Novi Pazar, Serbia | ||
| 3Faculty of Electronic Engineering, Nis, Srbia | ||
| چکیده | ||
| Let $G$ be a simple connected graph with degree sequence $(d_1,d_2,\ldots, d_n)$ where $\Delta =d_1\geq d_2\geq\cdots\geq d_n=\delta >0$ and let $\mu_1\geq \mu_2\geq\cdots\geq\mu_{n-1}>\mu_n=0$ be the Laplacian eigenvalues of $G$. Let $Kf(G)=n\sum_{i=1}^{n-1} \frac{1}{\mu_i}$ and $\tau(G)=\frac 1n \prod_{i=1}^{n-1} \mu_i$ denote the Kirchhoff index and the number of spanning trees of $G$, respectively. In this paper we establish several lower bounds for $Kf(G)$ in terms of $\tau(G)$, the order, the size and maximum degree of $G$. | ||
| کلیدواژهها | ||
| Topological indices؛ Kirchhoff index؛ spanning trees | ||
| مراجع | ||
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