Maximum nullity and zero forcing of circulant graphs

Linh Duong, Brenda K. Kroschel, Michael Riddell, Kevin N. Vander Meulen, Adam Van Tuyl

Published 2019-06-07Version 1

It is well-known that the zero forcing number of a graph provides a lower bound on the minimum rank of a graph. In this paper we bound and characterize the zero forcing number of certain circulant graphs, including some bipartite circulants, cubic circulants, and circulants which are torus products, to obtain bounds on the minimum rank and the maximum nullity. We also evaluate when the zero forcing number will give equality.