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On the Laplacian coefficients of acyclic graphs

✍ Scribed by Bojan Mohar

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
121 KB
Volume
422
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let G be a graph of order n and let (G, Ξ») = n k=0 (-1) k c k Ξ» n-k be the characteristic polynomial of its Laplacian matrix. Zhou and Gutman recently proved that among all trees of order n, the kth coefficient c k is largest when the tree is a path, and is smallest for stars. A new proof and a strengthening of this result is provided. A relation to the Wiener index is discussed.

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