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 \(n\rightarrow \infty .\)

在本论文中，我们研究了的图形无限族的复杂\（H_n = H_n（G_1，\，G_2，\ ldots，跨导）\）作为循环叶状结构获得以上的曲线图ħ上米与纤维顶点\（G_1 ，\，G_2，\ ldots，跨导。\）每个纤维\（的G_i = C_N（S_ {I，1}，\，S_ {I，2}，\ ldots，S_ {I，K_I}）\）的这个叶面是具有跳跃\（s_ {i，1}，\，s_ {i，2}，\ ldots，s_ {i，k_i}。\\的n个顶点上的循环图。）该族包括广义Petersen图族，I图，循环图的三明治，离散环面图等。我们为以下生成树的数量\（\ tau（n）\）获得一个封闭式根据Chebyshev多项式\（H_n \），研究此函数的一些算术性质，并找到其渐近性为\（n \ rightarrow \ infty。\）