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A note on multiplicity of the Laplacian eigenvalue of trees

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2 Author(s)
Zhenye Xu ; Sch. of Appl. Math., Univ. of Electron. Sci. & Technol. of China, Chengdu, China ; Chun Yang

Considering the multiplicity mT(¿) of eigenvalue ¿ (which equals 1) of Laplacian matrix of all trees, we get three results: When mT(1) equals n-2, the tree is unique, that is star graph K1, n-1; (ii) there exists no trees satisfying mT(1) equals n-3; (iii) When mT(1) equals n-4, this kind of trees are divided into two types. According to the process of proving, we devise a method to construct trees on some desired properties, which have practical value.

Published in:

Apperceiving Computing and Intelligence Analysis, 2009. ICACIA 2009. International Conference on

Date of Conference:

23-25 Oct. 2009