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A spanning tree of the 2m-dimensional hypercube with maximum number of degree-preserving vertices

โœ Scribed by Sul-young Choi; Puhua Guan


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
190 KB
Volume
117
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


For an n-dimensional hypercube Q., the maximum number of degree-preserving vertices in a spanning tree is 2"jn if n = 2" for an integer M. (If n # 2", then the maximum number of degree-preserving vertices in a spanning tree is less than 2"/n.) We also construct a spanning tree of Qzm with maximum number of degree-preserving vertices.


๐Ÿ“œ SIMILAR VOLUMES


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โœ Jerzy Topp; Preben D. Vestergaard ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 611 KB

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

A lower bound on the number of spanning
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If a graph G with cycle rank p contains both spanning trees with rn and with n end-vertices, rn < n, then G has at least 2p spanning trees with k end-vertices for each integer k, rn < k < n. Moreover, the lower bound of 2p is best possible. [ l ] and Schuster [4] independently proved that such span