Year: 2014
Type: preprint
Abstract: A P-set of a symmetric matrix $A$ is a set $α$ of indices such that the nullity of the matrix obtained from $A$ by removing rows and columns indexed by $α$ is $|α|$ more than that of $A$. It is known that each subset of a P-set is a P-set. It is also known that a set of indices such that each singleton subset is a P-set need not be a P-set. This note shows that if all pairs of vertices of a set with at least two elements are P-sets, then the set is a P-set.
Source: arXiv (Cornell University)
Authors: Nelson, Curtis G., Shader, Bryan L.
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394664813