Zero Forcing Sets and Bipartite Circulants

TL;DR

This paper studies bipartite circulant graphs, introducing a class with circulant biadjacency matrices, and characterizes those achieving minimal zero forcing numbers based on their parameters.

Contribution

It defines a new class of bipartite circulant graphs and provides bounds and characterizations for their zero forcing numbers.

Findings

Computed bounds for zero forcing numbers based on biadjacency matrix parameters

Characterized bipartite circulant graphs that attain the lower zero forcing bound

Described properties of regular bipartite graphs with circulant biadjacency matrices

Abstract

In this paper we introduce a class of regular bipartite graphs whose biadjacency matrices are circulant matrices and we describe some of their properties. Notably, we compute upper and lower bounds for the zero forcing number for such a graph based only on the parameters that describe its biadjacency matrix. The main results of the paper characterize the bipartite circulant graphs that achieve equality in the lower bound.