On the rank of a matrix associated with a graph.
Let \(X\) be a real symmetric matrix indexed by the vertices of a graph \(G\) such that all its diagonal entries are \(1\), \(X_{ij}= 0\) whenever vertices \(i\), \(j\) are non-adjacent and \(| X_{ij}|\leq 1\) for all other entries of \(X\). Let \(r(G)\) be the minimum possible rank of the matrix \(X\). The author studies relations between \(r(G)\) and several other graph invariants including the independence number, the chromatic number of the complement, the Lovász theta function and the Colin de Verdière number.
scientific article; zbMATH DE number 2041903