an:00059198
Zbl 0766.05036
Koganov, L. M.
Coding and counting spanning trees in Kleitman-Golden graphs
EN
Cybernetics 27, No. 3, 311-319 (1991); translation from Kibernetika 1991, No. 3, 1-7 (1991).
00180804
1991
j
05C30 05C05 11B39
Fibonacci numbers; spanning trees; Fibonacci sequence; direct coding; Kleitman-Golden graphs; words
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 \textit{S. D. Bedrosian} [J. Franklin Inst. 295, 175-177 (1973; Zbl 0298.05104)], \textit{D. J. Kleitman} and \textit{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.
M.??koviera (Bratislava)
Zbl 0298.05104