# The complements of path and cycle are determined by their distance (signless) Laplacian spectra

The complements of path and cycle are determined by their distance (signless) Laplacian spectra Let G be a connected graph with vertex set V(G) and edge set E(G). Let T(G) be the diagonal matrix of vertex transmissions of G and D(G) be the distance matrix of G. The distance Laplacian matrix of G is defined as L(G)=T(G)−D(G). The distance signless Laplacian matrix of G is defined as Q(G)=T(G)+D(G). In this paper, we show that the complements of path and cycle are determined by their distance (signless) Laplacian spectra. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

# The complements of path and cycle are determined by their distance (signless) Laplacian spectra

, Volume 328 – Jul 1, 2018
7 pages

/lp/elsevier/the-complements-of-path-and-cycle-are-determined-by-their-distance-Sah2hxBwmC
Publisher
Elsevier
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.034
Publisher site
See Article on Publisher Site

### Abstract

Let G be a connected graph with vertex set V(G) and edge set E(G). Let T(G) be the diagonal matrix of vertex transmissions of G and D(G) be the distance matrix of G. The distance Laplacian matrix of G is defined as L(G)=T(G)−D(G). The distance signless Laplacian matrix of G is defined as Q(G)=T(G)+D(G). In this paper, we show that the complements of path and cycle are determined by their distance (signless) Laplacian spectra.

### Journal

Applied Mathematics and ComputationElsevier

Published: Jul 1, 2018

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