G-2012-26
Two Laplacians for the Distance Matrix of a Graph
and BibTeX reference
We introduce a Laplacian and a signless Laplacian for the distance matrix of a connected graph, called the distance Laplacian and distance signless Laplacian, respectively. We show the equivalence between the distance signless Laplacian, distance Laplacian and the distance spectra for the class of transmission regular graphs. There is also an equivalence between the Laplacian spectrum and the distance Laplacian spectrum of any connected graph of diameter 2. Similarities between n, as a distance Laplacian eigenvalue, and the algebraic connectivity are established.
Published May 2012 , 15 pages
This cahier was revised in February 2013
Research Axis
Research applications
Publication
Jul 2013
Two Laplacians for the distance matrix of a graph
and
Linear Algebra and its Applications, 439(1), 21–33, 2013
BibTeX reference