TY - JOUR

T1 - On distance Laplacian and distance signless Laplacian eigenvalues of graphs

AU - Das, Kinkar Ch

AU - Aouchiche, Mustapha

AU - Hansen, Pierre

N1 - Funding Information:
The first author was supported by the Sungkyun Research Fund, Sungkyunkwan University, 2017, and National Research Foundation of the Korean government with grant No. 2017R1D1A1B03028642. The authors are grateful to the anonymous referee for helpful suggestions and valuable comments, which led to an improvement of the original manuscript.
Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2019/11/2

Y1 - 2019/11/2

N2 - Let D(G),DL(G) = Diag(Tr) − D(G) and DQ(G) = Diag(Tr) + D(G) be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph G, where Diag(Tr) denotes the diagonal matrix of the vertex transmissions in G. The eigenvalues of of DL(G) andDQ(G) will be denoted by (Formula presented.) and (Formula presented.), respectively. In this paper, we study the properties of the distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of graph G.

AB - Let D(G),DL(G) = Diag(Tr) − D(G) and DQ(G) = Diag(Tr) + D(G) be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph G, where Diag(Tr) denotes the diagonal matrix of the vertex transmissions in G. The eigenvalues of of DL(G) andDQ(G) will be denoted by (Formula presented.) and (Formula presented.), respectively. In this paper, we study the properties of the distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of graph G.

KW - 05C05

KW - Distance Laplacian eigenvalues

KW - diameter

KW - distance signless Laplacian eigenvalues

KW - domination number

KW - independence number

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U2 - 10.1080/03081087.2018.1491522

DO - 10.1080/03081087.2018.1491522

M3 - Article

AN - SCOPUS:85049634232

VL - 67

SP - 2307

EP - 2324

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 11

ER -