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Signless Laplacian state transfer on Q-graphs

Author

Listed:
  • Zhang, Xiao-Qin
  • Cui, Shu-Yu
  • Tian, Gui-Xian

Abstract

For a simple graph G, its Q-graph Q(G) is derived from G by adding one new point in every edge of G and linking two new vertices by edge if they are between two edges that having a common endpoint. In our work, we demonstrate that for a regular graph G, if all the signless Laplacian eigenvalues are integers, then the Q(G) exists no signless Laplacian perfect state transfer. We also present a sufficient restriction that the Q(G) admits signless Laplacian pretty good state transfer when G exhibits signless Laplacian perfect state transfer between two specific vertices for a regular graph G. In addition, in view of these results, we also present some new families of Q-graphs, which have no signless Laplacian perfect state transfer, but admit signless Laplacian pretty good state transfer.

Suggested Citation

  • Zhang, Xiao-Qin & Cui, Shu-Yu & Tian, Gui-Xian, 2022. "Signless Laplacian state transfer on Q-graphs," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001369
    DOI: 10.1016/j.amc.2022.127070
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    References listed on IDEAS

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    1. 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.
    2. Li, Yipeng & Liu, Xiaogang & Zhang, Shenggui, 2020. "Laplacian state transfer in Q-graph," Applied Mathematics and Computation, Elsevier, vol. 384(C).
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