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.
|الصفحات (من إلى)||774-787|
|دورية||Linear and Multilinear Algebra|
|المعرِّفات الرقمية للأشياء|
|حالة النشر||Published - أبريل 3 2015|
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