Abstract
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.
Original language | English |
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Pages (from-to) | 21-33 |
Number of pages | 13 |
Journal | Linear Algebra and Its Applications |
Volume | 439 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jun 1 2013 |
Externally published | Yes |
Keywords
- Distance matrix
- Eigenvalues
- Graph
- Laplacian
- Signless Laplacian
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics