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On distance Laplacian spectral determination of complete multipartite graphs

Author

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  • Rakshith, B.R.
  • Das, Kinkar Chandra

Abstract

The (distance) Laplacian spectrum is said to determine a graph Γ if there is no non-isomorphic graph whose (distance) Laplacian spectra is same as that of Γ. Aouchiche et al. [3] proved that “complete k-partite graph is determined by its distance Laplacian spectrum”. This result is not true. In this paper, we determine the correct result on this. Further motivated by this, the distance Laplacian spectral determination of complete k-partite graph with edge addition is studied and at last it is shown that the graphs whose complements are disconnected and determined by their Laplacian spectra are also determined by their distance Laplacian spectra.

Suggested Citation

  • Rakshith, B.R. & Das, Kinkar Chandra, 2023. "On distance Laplacian spectral determination of complete multipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    • Handle: RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008554
    DOI: 10.1016/j.amc.2022.127787
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    References listed on IDEAS

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    1. 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.
    2. Aouchiche, Mustapha & Hansen, Pierre, 2018. "Cospectrality of graphs with respect to distance matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 309-321.
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