Complexity of Discrete Seifert Foliations over a Graph

Abstract—We study the complexity of an infinite family of graphs $null$ that are discrete Seifert foliations over a given graph H on m vertices with fibers $null$ Each fiber G_i = $null$ of this foliation is a circulant graph on n vertices with jumps $null$ The family of discrete Seifert foliations is sufficiently large. It includes the generalized Petersen graphs, I-graphs, Y-graphs, H-graphs, sandwiches of circulant graphs, discrete torus graphs, and other graphs. A closed-form formula for the number $null$ of spanning trees in H_n is obtained in terms of Chebyshev polynomials, some analytical and arithmetic properties of this function are investigated, and its asymptotics as $null$ is determined.