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IEICE TRANSACTIONS on Fundamentals

Properties on the Average Number of Spanning Trees in Connected Spanning Subgraphs for an Undirected Graph

Peng CHENG, Shigeru MASUYAMA

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Summary :

Consider an undirected graph G=(V,E) with n (=|V|) vertices and m (=|E|) edges. It is well-known that the problem of computing the sequence Nn-1,Nn,...,Nm is #P-complete (see e.g.,[3]), where Ni denotes the number of connected spanning subgraphs with i (n-1!im) edges in G. In this paper, by proving new inequalities on the sequence Nn-1,Nn,...,Nm, we show an interesting and stronger property that the sequence γn-1n,...,γm, where γi denotes the average number of spanning trees in the connected spanning subgraphs with i edges, is a convex sequence as well as a monotonically increasing sequence, although this property does not hold for the sequence Nn-1,Nn,...,Nm.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.5 pp.1027-1033
Publication Date
2003/05/01
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Type of Manuscript
Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
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