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Minimizing the least eigenvalue of unicyclic graphs with fixed diameter |
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| Authors: | Mingqing Zhai Ruifang Liu |
| Institution: | a Department of Mathematics, East China Normal University, Shanghai, 200241, China b Department of Mathematics, Chuzhou University, Anhui, Chuzhou, 239012, China c Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China |
| Abstract: | Let U(n,d) be the set of unicyclic graphs on n vertices with diameter d. In this article, we determine the unique graph with minimal least eigenvalue among all graphs in U(n,d). It is found that the extremal graph is different from that for the corresponding problem on maximal eigenvalue as done by Liu et al. H.Q. Liu, M. Lu, F. Tian, On the spectral radius of unicyclic graphs with fixed diameter, Linear Algebra Appl. 420 (2007) 449-457]. |
| Keywords: | Unicyclic graph Least eigenvalue Diameter |
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