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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.

, 15 pages

This cahier was revised in February 2013

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Two Laplacians for the distance matrix of a graph
and
Linear Algebra and its Applications, 439(1), 21–33, 2013 BibTeX reference