Number of spanning trees in a wheel
- 1 March 1971
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuit Theory
- Vol. 18 (2) , 280-282
- https://doi.org/10.1109/tct.1971.1083273
Abstract
A recurrence relation for the number of spanning treesf(n)in the wheelW_{k},wheren \geq 3, is obtained asf(n+1)-f(n)=L_{2^{n}+1},wheref(3)=16and whereL_{k}is thekth number in the Lucas series1, 3, 4, 7, \cdots , L_{k}, \cdots ,whereL_{k} = L_{k+1} L_{k-1}fork > 1. Alternately,f(n) =L_{k}^{2} - 4 \deltawhere\delta = 0fornodd and1forneven, thus confirmingf(n)as a square number fornodd and serving to verify a previous finding in 1969 by Sedlacek thatf(n)=((3 + \sqrt{5})^{n} + (3 - \sqrt{5})^{n}/2^{n}-2.Keywords
This publication has 5 references indexed in Scilit:
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