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

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  • Xue, Jie
  • Liu, Shuting
  • Shu, Jinlong

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.

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  • Xue, Jie & Liu, Shuting & Shu, Jinlong, 2018. "The complements of path and cycle are determined by their distance (signless) Laplacian spectra," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 137-143.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:137-143
    DOI: 10.1016/j.amc.2018.01.034
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Discussion Paper 2007-33, Tilburg University, Center for Economic Research.
    2. van Dam, E.R. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Rakshith, B.R. & Das, Kinkar Chandra, 2023. "On distance Laplacian spectral determination of complete multipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 443(C).

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