The controllability of graphs with diameter n−2

作者：

Highlights：

• Characterizing the controllability of graphs with diameter n-2 and give a necessary and sufficient condition determining non-main eigenvalue of graphs.

• Geting the proportion of controllable graphs among the graphs with diameter n-2 by statistical methods, which partly verifies a conjecture.

• Giving a visualization method for characterizing controllable graph by controllability pattern.

摘要

•Characterizing the controllability of graphs with diameter n-2 and give a necessary and sufficient condition determining non-main eigenvalue of graphs.•Geting the proportion of controllable graphs among the graphs with diameter n-2 by statistical methods, which partly verifies a conjecture.•Giving a visualization method for characterizing controllable graph by controllability pattern.

论文关键词：Controllable graph,Adjacency spectrum,Main eigenvalue,Diameter

论文评审过程：Received 6 February 2021, Revised 11 April 2021, Accepted 14 April 2021, Available online 18 May 2021, Version of Record 18 May 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126327