G-2017-97
On distance Laplacian and distance signless Laplacian eigenvalues of graphs
, , and BibTeX reference
Let \({\mathcal D(G)}\)
, \({\mathcal D}^L(G)={\mathcal Diag(Tr)} - {\mathcal D(G)}\)
and \({\mathcal D}^Q(G)={\mathcal Diag(Tr)} + {\mathcal D(G)}\)
be, respectively, the distance matrix, the distance Laplacian matrix and the distance signless Laplacian matrix of graph \(G\)
, where
\({\mathcal Diag(Tr)}\)
denotes the diagonal matrix of the vertex transmissions in \(G\)
. The eigenvalues of \({\mathcal D}^L(G)\)
and \({\mathcal D}^Q(G)\)
will be denoted by
\(\partial^L_1 \geq \partial^L_2 \geq \cdots \geq \partial^L_{n-1} \geq \partial^L_n=0\)
and \(\partial^Q_1 \geq \partial^Q_2 \geq \cdots \geq \partial^Q_{n-1} \geq \partial^Q_n\)
,
respectively. In this paper we study the properties of the distance Laplacian eigenvalues and the distance signless Laplacian eigenvalues of graph \(G\)
.
Published November 2017 , 19 pages
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