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Coding and counting spanning trees in Kleitman-Golden graphs. (English. Russian original) Zbl 0766.05036
Cybernetics 27, No. 3, 311-319 (1991); translation from Kibernetika 1991, No. 3, 1-7 (1991).
A Kleitman-Golden graph of order \(n\) arises from the \(n\)-cycle \(C_ n\) by joining every pair of vertices at distance 2 with an edge. Answering a question of S. D. Bedrosian [J. Franklin Inst. 295, 175-177 (1973; Zbl 0298.05104)], D. J. Kleitman and B. Golden showed that the number of spanning trees of this graph is \(nf^ 2_ n\), where \((f_ n)_{n\geq 1}\) is the Fibonacci sequence defined by the initial conditions \(f_ 1=f_ 2=1\). The paper gives another proof of this fact, based on a direct coding of spanning trees in Kleitman-Golden graphs by words in a three letter alphabet.

MSC:
05C30 Enumeration in graph theory
05C05 Trees
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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