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The numbers of spanning trees of the cubic cycle \(C_ n^ 3\) and the quadruple cycle \(C_ n^ 4\). (English) Zbl 0879.05036

The paper considers the numbers of spanning trees of the cubic cycle \(C^3_n\) and the quadruple cycle \(C^4_n\). In addition, two recursive relations are presented.

MSC:

05C30 Enumeration in graph theory
05C05 Trees
05C38 Paths and cycles
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References:

[1] Baron, G.; Prodinger, H.; Tichy, R. F.; Boesch, F. T.; Wang, J. F., The number of spanning trees in the square of a cycle, Fibonacci Quart., 258-264 (1985) · Zbl 0587.05040
[2] Boesch, F. T.; Wang, J. F., A conjecture on the number of spanning trees in the square of a cycle, (Notes from New York Graph Theory Day V (1982), New York Academy Sciences: New York Academy Sciences New York), 16
[3] Boesch, F. T.; Prodinger, H., Spanning tree formulas and Chebyshev polynomials, Graphs Combin., 2, 191-200 (1986) · Zbl 0651.05028
[4] Biggs, N., Algebraic Graph Theory (1976), Cambridge Univ. Press: Cambridge Univ. Press Cambridge
[5] Kleitman, D. J.; Golden, B., Counting trees in a certain class of graphs, Amer. Math. Monthly, 82, 40-44 (1975) · Zbl 0297.05123
[6] Yong, Xue-rong; Zhang, Fu-ji, A simple proof for the complexity of square cycle \(C_p^2\), J. Xinjiang Univ., 11, 12-16 (1994) · Zbl 1056.05515
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