Lovász theta type norms and operator systems

Autor:	Vern I. Paulsen, Carlos M. Ortiz
Rok vydání:	2015
Předmět:	Numerical Analysis Algebra and Number Theory Graph theory Theta function Squeeze theorem Combinatorics Discrete Mathematics and Combinatorics Geometry and Topology Isomorphism Bitwise operation Quotient Subspace topology MathematicsofComputing_DISCRETEMATHEMATICS Mathematics Operator system
Zdroj:	Linear Algebra and its Applications. 477:128-147
ISSN:	0024-3795
DOI:	10.1016/j.laa.2015.03.022
Popis:	To each graph on n vertices there is an associated subspace of the n × n matrices called the operator system of the graph. We prove that two graphs are isomorphic if and only if their corresponding operator systems are unitally completely order isomorphic. This means that the study of graphs is equivalent to the study of these special operator systems up to the natural notion of isomorphism in their category. We define new graph theory parameters via this identification. Certain quotient norms that arise from studying the operator system of a graph give rise to a new family of parameters of a graph. We then show basic properties about these parameters and write down explicitly how to compute them via a semidefinite program, and discuss their similarities to the Lovasz theta function. Finally, we explore a particular parameter in this family and establish a sandwich theorem that holds for some graphs.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4194e091281d3ce63de5220483e36e15 https://doi.org/10.1016/j.laa.2015.03.022 Zobrazit plný text záznamu Full Text from ScienceDirect