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A note on the second largest eigenvalue of a tree with perfect matchings

โœ Scribed by Ji-Ming Guo; Shang-Wang Tan


Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
201 KB
Volume
380
Category
Article
ISSN
0024-3795

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A note on the number of perfect matching
โœ Zhang Fuji; Zhang Heping ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 484 KB

Let G be a bipartite graph with 2n vertices, A its adjacency matrix and K the number of perfect matchings. For plane bipartite graphs each interior face of which is surrounded by a circuit of length 4s + 2, s E { 1,2,. . .}, an elegant formula, i.e. det A = (-1 )nK2, had been rigorously proved by Cv