This report will present a new method for obtaining exact formulas for the number of marked spanning forests f(n) for an infinite family graphs H_n = H_n(G₁, G₂,...,G_m) obtained as a circulant foliation over graph H with m vertices and fibers G₁, G₂,...,G_m. Each such layer in turn, is a circulant graph with n vertices. Given the family includes generalized Petersen graphs, I-graphs, sandwiches of circulant graphs, graphs of discrete tori, etc. Obtained formulas are presented in terms of Chebyshev polynomials, which helps in establishing some of their arithmetic properties, as well as in study of their asymptotic behavior.

graphs, spanning forests, spanninng trees, circulant foilation

Mednykh Ilya Alexandrovich,  Novosibirsk State University

Grunvald Lilia Alexandrovna,  Novosibirsk State University