On the sum of signless Laplacian eigenvalues of a graph
نویسندگان
چکیده
For a simple graph G, let e(G) denote the number of edges and Sk(G) denote the sum of the k largest eigenvalues of the signless Laplacian matrix of G. We conjecture that for any graph G with n vertices, Sk(G) ≤ e(G) + k+1 2 for k = 1, . . . , n. We prove the conjecture for k = 2 for any graph, and for all k for regular graphs. The conjecture is an analogous to a conjecture by A.E. Brouwer with a similar statement but for the eigenvalues of Laplacian matrices of graphs. AMS Classification: 05C50
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