The Laplacian spread of quasi-tree graphs |
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Authors: | Ying Xu Jixiang Meng |
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Institution: | a College of Mathematics and Systems Science, Xinjiang University, Urumqi, Xinjiang 830046, PR China b Department of Applied Mathematics, Xinjiang University of Finance and Economics, Urumqi, Xinjiang 830012, PR China |
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Abstract: | The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second-smallest eigenvalue of the Laplacian matrix of the graph. Bao, Tan and Fan Y.H. Bao, Y.Y. Tan,Y.Z. Fan, The Laplacian spread of unicyclic graphs, Appl. Math. Lett. 22 (2009) 1011-1015.] characterize the unique unicyclic graph with maximum Laplacian spread among all connected unicyclic graphs of fixed order. In this paper, we characterize the unique quasi-tree graph with maximum Laplacian spread among all quasi-tree graphs in the set Q(n,d) with . |
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Keywords: | 05C50 15A18 |
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