𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Permanent of the Laplacian matrix of trees and bipartite graphs

✍ Scribed by Richard A Brualdi; John L Goldwasser

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
805 KB
Volume
48
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

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.

Bipartite labelings of trees and the gra
Bipartite labelings of trees and the gracesize
✍ Alexander Rosa; Jozef Ε irÑň πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 681 KB

## Abstract Let __T__ = (__V, E__) be a tree whose vertices are properly 2‐colored. A bipartite labeling of __T__ is a bijection __f__: __V__ ← {0, 1, ⃛, | __E__ |} for which there is a __k__ such that whenever __f__(__u__) ≀ __k__ < __f__(__v__), then __u__ and __v__ have different colors. The α‐s