The number of rooted forests in circulant graphs
The number of rooted forests in circulant graphs
In this paper, we develop a new method to produce explicit formulas for the number fG(n) of rooted spanning forests in the circulant graphs G = Cn(s1,s2,…,sk) and G = C2n(s1,s2,…,sk,n). These formulas are expressed through Chebyshev polynomials. We prove that in both cases the number of rooted spanning forests …