## Abstract Motivated by the observation that the sparse treeβlike subgraphs in a small world graph have large diameter, we analyze random spanning trees in a given host graph. We show that the diameter of a random spanning tree of a given host graph __G__ is between and with high probability., w
Transformations of a Graph Increasing its Laplacian Polynomial and Number of Spanning Trees
β Scribed by A.K. Kelmans
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 310 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0195-6698
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π SIMILAR VOLUMES
The quantum mechanical relevance of the concept of a spanning tree extant within a given molecular graph-specifically, one that may be considered to represent the carbon-atom connectivity of a particular (planar) conjugated system-was first explicitly pointed out by Professor Roy McWeeny in his now-
## Abstract Given a graph where increasing the weight of an edge has a nondecreasing convex piecewise linear cost, we study the problem of finding a minimum cost increase of the weights so that the value of all minimum spanning trees is equal to some target value. Frederickson and SolisβOba gave an
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