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Laplacian coefficients of trees with a given bipartition

✍ Scribed by Weiqi Lin; Weigen Yan

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
658 KB
Volume
435
Category
Article
ISSN
0024-3795

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πŸ“œ SIMILAR VOLUMES

Trees with minimal Laplacian coefficient
Trees with minimal Laplacian coefficients
✍ Aleksandar IliΔ‡ πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 408 KB

Let G be a simple undirected graph with the characteristic polynomial of its Laplacian matrix L(G), P(G, Β΅) = n k=0 (-1) k c k Β΅ n-k . It is well known that for trees the Laplacian coefficient c n-2 is equal to the Wiener index of G, while c n-3 is equal to the modified hyper-Wiener index of the gra

Permanent of the laplacian matrix of tre
Permanent of the laplacian matrix of trees with a given matching
✍ John L Goldwasser πŸ“‚ Article πŸ“… 1986 πŸ› Elsevier Science 🌐 English βš– 715 KB

We define the Laplacian ratio of a tree z(T), to be the permanent of the Laplacian matrix of T divided by the product of the degrees of the vertices. Best possible lower and upper bounds are obtained for ~r(T) in terms of the size of the largest matching in T.

Permanent of the Laplacian matrix of tre
Permanent of the Laplacian matrix of trees and bipartite graphs
✍ Richard A Brualdi; John L Goldwasser πŸ“‚ Article πŸ“… 1984 πŸ› Elsevier Science 🌐 English βš– 805 KB

be the Laplacian matrix of G. When G is a tree or a bipartite graph we obtain bounds for the permanent of L(G) both in terms of n only and in terms of d 1 ..... d,. Improved bounds are obtained in terms of the diameter of T and the size of a matching in T.