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The smallest values of algebraic connectivity for unicyclic graphs |
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| Authors: | Jianxi Li Ji-Ming Guo |
| Institution: | a Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou, Fujian, China b Department of Mathematics, Hong Kong Baptist University, 224 Waterloo Road, Kowloon Tong, Hong Kong, China c Department of Applied Mathematics, China University of Petroleum, Dongying, Shandong, China |
| Abstract: | The algebraic connectivity of G is the second smallest eigenvalue of its Laplacian matrix. Let Un be the set of all unicyclic graphs of order n. In this paper, we will provide the ordering of unicyclic graphs in Un up to the last seven graphs according to their algebraic connectivities when n≥13. This extends the results of Liu and Liu Y. Liu, Y. Liu, The ordering of unicyclic graphs with the smallest algebraic connectivity, Discrete Math. 309 (2009) 4315-4325] and Guo J.-M. Guo, A conjecture on the algebraic connectivity of connected graphs with fixed girth, Discrete Math. 308 (2008) 5702-5711]. |
| Keywords: | Unicyclic graph Algebraic connectivity Order |
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