Suppose that A is a real symmetric matrix of order n. Denote by m_{A}(0) the nullity of A. For a nonempty subset α of {1, 2,..., n}, let A(α) be the principal submatrix of A obtained from A by deleting the rows and columns indexed by α. When m_{A(\alpha )}(0) = m_{A}(0)+|α|, we call α a P-set of A. It is known that every P-set of A contains at most \left \lfloor n/2 \right \rfloorelements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step to the full characterization of these graphs of odd order, we establish some conditions for such graphs G under which there is a real symmetric matrix A whose graph is G and contains a P-set of size (n − 1)/2., Zhibin Du, Carlos M. da Fonseca., and Obsahuje seznam literatury