Bounds on minimum semidefinite rank of graphs

Sivaram K. Narayan, Yousra Sharawi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The minimum semidefinite rank (Formula presented.) of a graph is defined to be the minimum rank among all Hermitian positive semidefinite matrices associated to the graph. A problem of interest is to find upper and lower bounds for (Formula presented.) of a graph using known graph parameters such as the independence number and the minimum degree of the graph. We provide a sufficient condition for (Formula presented.) of a bipartite graph to equal its independence number. The delta conjecture gives an upper bound for (Formula presented.) of a graph in terms of its minimum degree. We present classes of graphs for which the delta conjecture holds.

Original languageEnglish
Pages (from-to)774-787
Number of pages14
JournalLinear and Multilinear Algebra
Volume63
Issue number4
DOIs
Publication statusPublished - Apr 3 2015

Fingerprint

Graph in graph theory
Independence number
Minimum Degree
Minimum Rank
Positive Semidefinite Matrix
Bipartite Graph
Upper and Lower Bounds
Upper bound
Sufficient Conditions

Keywords

  • connectivity of a graph
  • delta conjecture
  • independence number
  • matrix of a graph
  • minimum semidefinite rank

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Bounds on minimum semidefinite rank of graphs. / Narayan, Sivaram K.; Sharawi, Yousra.

In: Linear and Multilinear Algebra, Vol. 63, No. 4, 03.04.2015, p. 774-787.

Research output: Contribution to journalArticle

Narayan, Sivaram K. ; Sharawi, Yousra. / Bounds on minimum semidefinite rank of graphs. In: Linear and Multilinear Algebra. 2015 ; Vol. 63, No. 4. pp. 774-787.
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