We consider a family of graphs Hn(s1, ..., sk; t1, ..., tl) that is a generalisation of the family of I-graphs, which, in turn, includes the generalized Petersen graphs. We present an explicit formula for the number τ(n) of spanning trees in these graphs in terms of the Chebyshev polynomials and find its asymptotics. Also, we show that the number of spanning trees can be represented in the form τ(n) = p n a(n)2; where a(n) is an integer sequence and p is a prescribed integer depending on the number of even elements in the sequence s1, ..., sk; t1, ..., tl and the parity of n.
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- 1.01 МАТЕМАТИКА