Campus Units
Mathematics
Document Type
Article
Publication Version
Published Version
Publication Date
2010
Journal or Book Title
Involve
Volume
3
DOI
10.2140/involve.2010.3.371
Abstract
The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ij-th entry (for i≠j) is nonzero whenever {i,j}{i,j} is an edge in G and is zero otherwise. Maximum nullity is taken over the same set of matrices, and the sum of maximum nullity and minimum rank is the order of the graph. The zero forcing number is the minimum size of a zero forcing set of vertices and bounds the maximum nullity from above. This paper defines the graph families ciclos and estrellas and establishes the minimum rank and zero forcing number of several of these families. In particular, these families provide examples showing that the maximum nullity of a graph and its dual may differ, and similarly for the zero forcing number.
Copyright Owner
The Authors
Copyright Date
2010
Language
en
File Format
application/pdf
Recommended Citation
Almodovar, Edgard; DeLoss, Laura; Hogben, Leslie; Hogenson, Kirsten; Murphy, Kaitlyn; Peters, Travis; and Ramírez, Camila A., "Minimum rank, maximum nullity and zero forcing number for selected graph families" (2010). Mathematics Publications. 90.
https://lib.dr.iastate.edu/math_pubs/90
Comments
This is an article from Involve 3 (2010): 371, doi:10.2140/involve.2010.3.371. Posted with permission.