Bicyclic graphs with maximum sum of the two largest Laplacian eigenvalues - Yirong Zheng; An Chang; Jianxi Li; Sa Rula (Journal of Inequalities and Applications, 2016)
Abstract Let G be a simple connected graph and S 2 ( G ) $S_{2}(G)$ be the sum of the two largest Laplacian eigenvalues of G. In this paper, we determine the bicyclic graph with maximum S 2 ( G ) $S_{2}(G)$ among all bicyclic graphs of order n, which confirms the conjecture of Guan et al. (J. Inequal. Appl. 2014:242, 2014) for the case of bicyclic graphs.