Let F(x)=∑∞n=1 Tsi,s2,...,sk(n)x^n be the generating function for the number,Ts1bs2,...,sk(n) of spanning trees in the circulant graph Cn(s1,S2,...,Sk).We show that F(x)is a rational function with integer coefficien...Let F(x)=∑∞n=1 Tsi,s2,...,sk(n)x^n be the generating function for the number,Ts1bs2,...,sk(n) of spanning trees in the circulant graph Cn(s1,S2,...,Sk).We show that F(x)is a rational function with integer coefficients satisfying the property F(x)=F(l/x).A similar result is also true for the circulant graphs C2n(s1,S2,....,Sk,n)of odd valency.We illustrate the obtained results by a series of examples.展开更多
基金The results of this work were partially supported by the Russian Foundation for Basic Research(grants 18-01-00420 and 18-501-51021).
文摘Let F(x)=∑∞n=1 Tsi,s2,...,sk(n)x^n be the generating function for the number,Ts1bs2,...,sk(n) of spanning trees in the circulant graph Cn(s1,S2,...,Sk).We show that F(x)is a rational function with integer coefficients satisfying the property F(x)=F(l/x).A similar result is also true for the circulant graphs C2n(s1,S2,....,Sk,n)of odd valency.We illustrate the obtained results by a series of examples.
