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A bound for the permanent of the Laplacian matrix

โœ Scribed by R.B. Bapat


Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
296 KB
Volume
74
Category
Article
ISSN
0024-3795

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๐Ÿ“œ SIMILAR VOLUMES


Permanent of the laplacian matrix of tre
โœ John L Goldwasser ๐Ÿ“‚ Article ๐Ÿ“… 1986 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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
โœ Richard A Brualdi; John L Goldwasser ๐Ÿ“‚ Article ๐Ÿ“… 1984 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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.

The Permanent Rank of a Matrix
โœ Yang Yu ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 91 KB

Define the perrank of a matrix A to be the size of the largest square submatrix of A with nonzero permanent. Motivated in part by the Alon Jaeger Tarsi Conjecture [3], we prove several results on perranks..