On the sum of the two largest Laplacian eigenvalues of unicyclic graphs

Abstract

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Let G be a simple graph and ...... be the sum of the two largest Laplacian eigenvalues of G. Guan et al. (J. Inequal. Appl. 2014:242, 2014) determined the largest value for ...... among all trees of order n. They also conjectured that among all connected graphs of order n with m (......) edges, ...... is the unique graph which has maximal value of ......, where ...... is a graph of order n with m edges which has ...... triangles with a common edge and ...... pendent edges incident with one end vertex of the common edge. In this paper, we confirm the conjecture with .......