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The controllability of graphs with diameter n−2

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  • Wei, Liang
  • Li, Faxu
  • Zhao, Haixing
  • Deng, Bo

Abstract

Controllable graphs are connected graphs in which all eigenvalues are mutually distinct and main. In this work, a new method of characterizing the controllability of graphs with diameter n−2 is presented. A necessary and sufficient condition determining non-main eigenvalue of graphs with diameter n−2 is obtained, and the controllability of two kinds of graphs with diameter n−2 is characterized. Besides, the visualization representation of statistical results of controllable graphs is presented, and they show that the proportion of controllable graphs among the graphs with diameter n−2 is stablely at 15%, which partly verifies a conjecture proposed by Stanić.

Suggested Citation

  • Wei, Liang & Li, Faxu & Zhao, Haixing & Deng, Bo, 2021. "The controllability of graphs with diameter n−2," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    • Handle: RePEc:eee:apmaco:v:407:y:2021:i:c:s0096300321004161
    DOI: 10.1016/j.amc.2021.126327
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    References listed on IDEAS

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    1. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
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