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Permanents of doubly stochastic trees

โœ Scribed by Mohammad H. Ahmadi; Jae-Hyun Baek; Suk-Geun Hwang

Book ID
104155473
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
111 KB
Volume
370
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

For a tree T of order n, let (T ) = {X โˆˆ n | X A(T ) + I n }, where n denotes the set of all doubly stochastic matrices of order n and A(T ) denotes the adjacency matrix of T , and let ยต(T ) denote the minimum permanent of matrices in (T ). Let P n denote the path of length n -1 and K 1,n-1 the complete bipartite graph on 1 + (n -1) vertices. In this paper, it is shown that P n and K 1,n-1 are the only trees with minimal and maximal ยต-values respectively among all trees of order n.

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