The controllability of graphs with diameter n−2

Liang Wei, Faxu Li, Haixing Zhao and Bo Deng

Applied Mathematics and Computation, 2021, vol. 407, issue C

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.

Keywords: Controllable graph; Adjacency spectrum; Main eigenvalue; Diameter (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:407:y:2021:i:c:s0096300321004161

DOI: 10.1016/j.amc.2021.126327

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