An edge-grafting theorem on Laplacian spectra of graphs and its application |
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| Authors: | Mingqing Zhai Ruifang Liu |
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| Affiliation: | 1. Department of Mathematics , East China Normal University , Shanghai, 200241, China;2. Department of Mathematics , Chuzhou University , Anhui, Chuzhou, 239012, China;3. Department of Mathematics , East China Normal University , Shanghai, 200241, China |
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| Abstract: | Let 𝒰(n,?d) be the class of unicyclic graphs on n vertices with diameter d. This article presents an edge-grafting theorem on Laplacian spectra of graphs. By applying this theorem, we determine the unique graph with the maximum Laplacian spectral radius in 𝒰(n,?d). This extremal graph is different from that for the corresponding problem on the adjacency spectral radius as done by Liu et al. Q. Liu, M. Lu, and F. Tian, On the spectral radius of unicyclic graphs with fixed diameter, Linear Algebra Appl. 420 (2007), 449–457]. |
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| Keywords: | edge-grafting Laplacian spectral radius diameter unicyclic graph |
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