Number of spanning trees in a wheel

Author

Myers, B.

Volume

Issue

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

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1168451