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Project Euclid
Other literature type . 2010
Data sources: Project Euclid
Involve a Journal of Mathematics
Article . 2010 . Peer-reviewed
Data sources: Crossref
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Minimum rank, maximum nullity and zero forcing number for selected graph families

Authors: Almodovar, Edgard; DeLoss, Laura; Hogben, Leslie; Hogenson, Kirsten; Murphy, Kaitlyn; Peters, Travis; Ramírez, Camila;

Minimum rank, maximum nullity and zero forcing number for selected graph families

Abstract

The minimum rank of a simple graph G is dened to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i 6 j) is nonzero whenever fi;jg 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 denes 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 the examples showing that the maximum nullity of a graph and its dual may dier, and similarly for zero forcing number.

Country
United States
Keywords

15A18, 330, dual, ciclo, estrella, 15A03, 510, minimum rank, Discrete Mathematics and Combinatorics, 05C50, zero forcing number, maximum nullity

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
Average
Green
bronze