Laplacian controllable graphs based on connecting two antiregular graphs
Shun‐Pin Hsu, Ping‐Yen Yang · IET Control Theory and Applications · 2018
The Laplacian controllability of combined graphs are studied. It is shown that an antiregular graph, namely, a connected simple graph with exactly two vertices having the same degree, can be connected to another antiregular graph by a newly added edge, and becomes a Laplacian controllable graph under one controller. The methods to identify the vertices connected by the new edge and to assign the control vectors that render the resulting graph Laplacian controllable are presented. Numerical examples are given to illustrate the authors work.