Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 4: 693 - 713

DOI: https://doi.org/10.1007/s11464-019-0779-3

RESEARCH ARTICLE

Distance signless Laplacian eigenvalues of graphs

  • Kinkar Chandra DAS , 1 ,
  • Huiqiu LIN 2 ,
  • Jiming GUO 2
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  • 1. Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
  • 2. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Received date: 12 Apr 2018

Accepted date: 21 Jun 2019

Published date: 15 Aug 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

Suppose that the vertex set of a graph G is V(G)={v1,v2,...,vn}. The transmission Tr(vi) (or Di) of vertex vi is defined to be the sum of distances from vi to all other vertices. Let Tr(G) be the n×n diagonal matrix with its (i, i)-entry equal to TrG(vi). 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 L(G)=Tr(G)+D(G), where D(G) 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.

Key words： Graph; distance signless Laplacian spectral radius; second largest eigenvalue of distance signless Laplacian matrix; spread

Cite this article

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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