科研之友
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摘要
For a simple graph G on n vertices and an integer k with 1 a (c) 1/2 k a (c) 1/2 n, denote by (G) the sum of k largest signless Laplacian eigenvalues of G. It was conjectured that (G) a (c) 1/2 e(G) + (k+1 2), where e(G) is the number of edges of G. This conjecture has been proved to be true for all graphs when k a {1, 2, n - 1, n}, and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all k). In this note, this conjecture is proved to be true for all graphs when k = n - 2, and for some new classes of graphs.
