The kth Laplacian eigenvalue of a tree |
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| Authors: | Ji‐Ming Guo |
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| Affiliation: | 1. Department of Applied Mathematics, China University of Petroleum, Shandong, Dongying 257061, China;2. Department of Applied Mathematics, Tongji University, Shanghai 200092, China |
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| Abstract: | Let λk(G) be the kth Laplacian eigenvalue of a graph G. It is shown that a tree T with n vertices has  and that equality holds if and only if k < n, k|n and T is spanned by k vertex disjoint copies of  , the star on  vertices. © 2006 Wiley Periodicals, Inc. J Graph Theory |
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| Keywords: | tree Laplacian eigenvalue spanning subgraph |
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