CP graphs and SPN graphs

A graph G is SPN if every copositive matrix realization of it is a sum of a positive semidefinite matrix and a nonnegative one (an SPN matrix).A graph is CP if every doubly nonnegative matrix realization of it is completely positive.This survey describes the current state of the problem of characterizing SPN graphs in comparison to the, by now classical, characterization of CP graphs, which inspired the attempt to define and study SPN graphs.

Publication Details

Journal
Communications in Optimization Theory
Published
2025-01-01
DOI
https://doi.org/10.23952/cot.2025.3
Primary Topic
Advanced Graph Theory Research
Type
article
Field-Weighted Citation Impact
0.00
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article

CP graphs and SPN graphs

Communications in Optimization Theory
Advanced Graph Theory Research
article

CP graphs and SPN graphs

article en

Abstract

A graph G is SPN if every copositive matrix realization of it is a sum of a positive semidefinite matrix and a nonnegative one (an SPN matrix).A graph is CP if every doubly nonnegative matrix realization of it is completely positive.This survey describes the current state of the problem of characterizing SPN graphs in comparison to the, by now classical, characterization of CP graphs, which inspired the attempt to define and study SPN graphs.

Communications in Optimization TheoryVol. 2025(1)
Openalex Percentile: Top 71%
Advanced Graph Theory Research
DOIOpen Access PDFOpenAlex
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CP graphs and SPN graphs · Communications in Optimization Theory (2025) | TGRS Research Map | TGRS