Notes on the sum of powers of the signless Laplacian eigenvalues of graphs

摘要

For a graph G and a non-zero real number alpha, the graph invariant S-alpha,(G) is the sum of the alpha th power of the non-zero signless Laplacian eigenvalues of G. In this paper, we obtain sharp bounds of S-alpha(G) for a connected bipartite graph G on n vertices and a connected graph G on n vertices having a connectivity less than or equal to k, respectively, and propose some open problems for future research.