On the largest kth eigenvalues of trees with n≡0 (mod k) |
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Authors: | Yong Zou Zheng Wang Xuerong Yong |
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Affiliation: | Department of Mathematics, Xinjiang University, Urumqi 830046, People's Republic of China |
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Abstract: | We consider the only remaining unsolved case n≡0 (mod k) for the largest kth eigenvalue of trees with n vertices. In 1995, Jia-yu Shao gave complete solutions for the cases k=2,3,4,5,6 and provided some necessary conditions for extremal trees in general cases (cf. [Linear Algebra Appl. 221 (1995) 131]). We further improve Shao's necessary condition in this paper, which can be seen as the continuation of [Linear Algebra Appl. 221 (1995) 131]. |
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Keywords: | Eigenvalues of a graph Extremal tree Induced subgraph |
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