DocumentCode :
1168451
Title :
Number of spanning trees in a wheel
Author :
Myers, B.
Volume :
18
Issue :
2
fYear :
1971
fDate :
3/1/1971 12:00:00 AM
Firstpage :
280
Lastpage :
282
Abstract :
A recurrence relation for the number of spanning trees f(n) in the wheel W_{k}, where n \\geq 3 , is obtained as f(n+1)-f(n)=L_{2^{n}+1}, where f(3)=16 and where L_{k} is the k th number in the Lucas series 1, 3, 4, 7, \\cdots , L_{k}, \\cdots , where L_{k} = L_{k+1} L_{k-1} for k > 1 . Alternately, f(n) =L_{k}^{2} - 4 \\delta where \\delta = 0 for n odd and 1 for n even, thus confirming f(n) as a square number for n odd and serving to verify a previous finding in 1969 by Sedlacek that f(n)=((3 + \\sqrt {5})^{n} + (3 - \\sqrt {5})^{n}/2^{n}-2 .
Keywords :
Network topology; Trees; Wheels; Bipartite graph; Circuit testing; Circuit theory; Contracts; Gold; Logistics; Moon; Transmission line matrix methods; Tree graphs; Wheels;
fLanguage :
English
Journal_Title :
Circuit Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9324
Type :
jour
DOI :
10.1109/TCT.1971.1083273
Filename :
1083273
Link To Document :
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