The controllability of graphs with diameter n−2

被引：0
|
作者：
Wei, Liang [1 ,2 ]
Li, Faxu [3 ]
Zhao, Haixing [3 ]
Deng, Bo [2 ]
机构：
[1] School of Computer Science, Shaanxi Normal University, Xi'an,710062, China
[2] School of Mathematics and Statistics, Qinghai Normal University, Xining,810008, China
[3] College of Computer, Qinghai Normal University, Xining,810008, China
来源：
Applied Mathematics and Computation | 2021年 / 407卷
基金：
中国国家自然科学基金;
关键词：
Eigenvalues and eigenfunctions - Graphic methods;
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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. © 2021 Elsevier Inc.
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