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On the number of spanning trees of circulant graphs. (English) Zbl 0554.05019
A circulant graph \(C_ n(k_ 1,k_ 2,...,k_ m)\) is a graph with n vetices numbered 0,1,...,n-1 and vertex j is adjacent to the 2m vertices \(j\pm k_ i\) (mod n-1). This paper finds a (complex) formula for the number of spanning trees of a circulant graph \(C_ n(k_ 1,k_ 2,...,k_ m)\). With this formula, the authors verify the following recent conjecture of Boesch: the number of spanning trees of \(C_ n(1,2)\) is \(nF^ 2_ n\), where \(F_ n\) is the n-th Fibonacci number (with \(F_ 0=0\), \(F_ 1=1)\).
Reviewer: A.Tucker

MSC:
05C05 Trees
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