Frontiers of Mathematics in China >
Distance signless Laplacian eigenvalues of graphs
Received date: 12 Apr 2018
Accepted date: 21 Jun 2019
Published date: 15 Aug 2019
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Suppose that the vertex set of a graph G is . The transmission (or Di) of vertex vi is defined to be the sum of distances from vi to all other vertices. Let be the diagonal matrix with its (i, i)-entry equal to . The distance signless Laplacian spectral radius of a connected graph G is the spectral radius of the distance signless Laplacian matrix of G, defined as , where is the distance matrix of G. In this paper, we give a lower bound on the distance signless Laplacian spectral radius of graphs and characterize graphs for which these bounds are best possible. We obtain a lower bound on the second largest distance signless Laplacian eigenvalue of graphs. Moreover, we present lower bounds on the spread of distance signless Laplacian matrix of graphs and trees, and characterize extremal graphs.
Kinkar Chandra DAS , Huiqiu LIN , Jiming GUO . Distance signless Laplacian eigenvalues of graphs[J]. Frontiers of Mathematics in China, 2019 , 14(4) : 693 -713 . DOI: 10.1007/s11464-019-0779-3
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