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Graphs with an extremal number of spanning trees

✍ Scribed by A. K. Kelmans

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
129 KB
Volume
4
Category
Article
ISSN
0364-9024

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πŸ“œ SIMILAR VOLUMES

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A note on graphs with diameter-preserving spanning trees
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The distance between a pair of vertices u, u in a graph G is the length of a shortest path joining u and u. The diameter diam(G) of G is the maximum distance between all pairs of vertices in G. A spanning tree Tof G is diameter preserving if diam(T) = diam(G). In this note, we characterize graphs th

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The following asymptotic estimation of the maximum number of spanning trees f k (n) in 2kregular circulant graphs ( k ΓΊ 1) on n vertices is the main result of this paper: )) , where

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Chvatal established that r(T,, K,,) = (m -1 ) ( n -1 ) + 1, where T, , , is an arbitrary tree of order m and K, is the complete graph of order n. This result was extended by Chartrand, Gould, and Polimeni who showed K, could be replaced by a graph with clique number n and order n + 5 provided n 2 3