On distance Laplacian and distance signless Laplacian eigenvalues of graphs. Issue 11 (2nd November 2019)

• Record Type: Journal Article
• Authors: Das, Kinkar Ch.; Aouchiche, Mustapha; Hansen, Pierre
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 11(2019)
• Page Start: 2307
• Page End: 2324
• Publication Date: 2019-11-02
• Subjects: Distance Laplacian eigenvalues -- distance signless Laplacian eigenvalues -- domination number -- independence number -- diameter; 05C05; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1491522
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: Let D ( G ), D L ( G ) = D i a g ( T r ) − D ( G ) and D Q ( G ) = D i a g ( T r ) + D ( G ) be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph G, where D i a g ( T r ) denotes the diagonal matrix of the vertex transmissions in G . The eigenvalues of D L ( G ) and D Q ( G ) will be denoted by ∂ 1 L ≥ ∂ 2 L ≥ ⋯ ≥ ∂ n − 1 L ≥ ∂ n L = 0 and ∂ 1 Q ≥ ∂ 2 Q ≥ ⋯ ≥ ∂ n − 1 Q ≥ ∂ n Q , respectively. In this paper, we study the properties of the distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of graph G .