Complexity of the circulant foliation over a graph
| Autor: | Kwon, Young Soo, Mednykh, Alexander, Mednykh, Ilya |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In the present paper, we investigate the complexity of infinite family of graphs $H_n=H_n(G_1,\,G_2,\ldots,G_m)$ obtained as a circulant foliation over a graph $H$ on $m$ vertices with fibers $G_{1},\,G_{2},\ldots,G_{m}.$ Each fiber $G_{i}=C_{n}(s_{i,1},\,s_{i,2},\ldots,s_{i,k_{i}})$ of this foliation is the circulant graph on $n$ vertices with jumps $s_{i,1},\,s_{i,2},\ldots,s_{i,k_{i}}.$ This family includes the family of generalized Petersen graphs, $I$-graphs, sandwiches of circulant graphs, discrete torus graphs and others. We obtain a closed formula for the number $\tau(n)$ of spanning trees in $H_{n}$ in terms of Chebyshev polynomials, investigate some arithmetical properties of this function and find its asymptotics as $n\to\infty.$ Comment: 14 pages |
| Databáze: | arXiv |
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