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Conference material: "Academician O.B. Lupanov XIV International Scientific Seminar "Discrete Mathematics and Its Applications" (20-25 June 2022, Moscow)"
Authors: Mednykh I.A., Grunvald L.A.
Number of labelled spanning forests for circulant foliation over graph
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 Hn = Hn(G1, G2,...,Gm) obtained as a circulant foliation over graph H with m vertices and fibers G1, G2,...,Gm. 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
Publication language: russian,  pages: 2 (p. 197-198)
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About authors:
  • Mednykh Ilya Alexandrovich,  Novosibirsk State University
  • Grunvald Lilia Alexandrovna,  Novosibirsk State University