Bounds on the sum of minimum semidefinite rank of a graph and its complement

Sivaram K. Narayan, Yousra Sharawi*

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةArticleمراجعة النظراء

ملخص

The minimum semi-definite rank (msr) of a graph is the minimum rank among all positive semi-definite matrices associated to the graph. The graph complement conjecture gives an upper bound for the sum of the msr of a graph and the msr of its complement. It is shown that when the msr of a graph is equal to its independence number, the graph complement conjecture holds with a better upper bound. Several sufficient conditions are provided for the msr of different classes of graphs to equal to its independence number.

اللغة الأصليةEnglish
رقم المقال31
الصفحات (من إلى)399-406
عدد الصفحات8
دوريةElectronic Journal of Linear Algebra
مستوى الصوت34
المعرِّفات الرقمية للأشياء
حالة النشرPublished - 2018
منشور خارجيًانعم

ASJC Scopus subject areas

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