Nearly symmetric-indecomposable matrices

Abstract

We introduce nearly symmetric-decomposable matrices, which are a symmetric analogue of nearly decomposable matrices. The defining matrix property is related to 2-matching covered and minimally 2-matching covered properties of a graph (possibly containing loops). We develop constructions and properties of nearly symmetric-decomposable -matrices, some of which relate to the location and number of nonzero entries on the main diagonal.