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On numbers of vertices of maximum degree in the spanning trees of a graph

✍ Scribed by Jerzy Topp; Preben D. Vestergaard

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 611 KB
Volume: 155
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00389-z

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✦ Synopsis

For a connected graph G, let ~-(G) be the set of all spanning trees of G and let nd(G) be the number of vertices of maximum degree in G. In this paper we show that if G is a cactus or a connected graph with p vertices and p+ 1 edges, then the set {na(T) : T C ~-(G)) has at most one gap, that is, it is a set of consecutive integers or it is the union of two sets each of which consists of consecutive integers.

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