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Article
Minimum rank, maximum nullity and zero forcing number for selected graph families
Involve
  • Edgard Almodovar, University of Puerto Rico, Río Piedras Campus
  • Laura DeLoss, Iowa State University
  • Leslie Hogben, Iowa State University
  • Kirsten Hogenson, University of North Dakota
  • Kaitlyn Murphy, Montclair State University
  • Travis Peters, Iowa State University
  • Camila A. Ramírez, University of Puerto Rico, Río Piedras Campus
Document Type
Article
Publication Version
Published Version
Publication Date
1-1-2010
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.

Comments

This is an article from Involve 3 (2010): 371, doi:10.2140/involve.2010.3.371. Posted with permission.

Copyright Owner
The Authors
Language
en
File Format
application/pdf
Citation Information
Edgard Almodovar, Laura DeLoss, Leslie Hogben, Kirsten Hogenson, et al.. "Minimum rank, maximum nullity and zero forcing number for selected graph families" Involve Vol. 3 (2010)
Available at: http://works.bepress.com/leslie-hogben/57/