On distance Laplacian and distance signless Laplacian eigenvalues of graphs. Issue 11 (2nd November 2019) - Das, Kinkar Ch.; Aouchiche, Mustapha; Hansen, Pierre
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 .