Zero forcing sets and bipartite circulants
Copyright policy )Zero forcing sets and bipartite circulants
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.
22 pages, 13 figures
- University of Wisconsin–Parkside United States
- University of Wisconsin–Oshkosh United States
- University of Wisconsin System United States
- University of Wisconsin–Madison United States
circulant matrix, Numerical Analysis, Algebra and Number Theory, Minimum rank, Circulant matrix, Maximum nullity, Zero forcing number, minimum rank, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 05C50 (Primary) 05C75, 15A03 (Secondary), Geometry and Topology, Combinatorics (math.CO), zero forcing number, maximum nullity, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
circulant matrix, Numerical Analysis, Algebra and Number Theory, Minimum rank, Circulant matrix, Maximum nullity, Zero forcing number, minimum rank, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 05C50 (Primary) 05C75, 15A03 (Secondary), Geometry and Topology, Combinatorics (math.CO), zero forcing number, maximum nullity, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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