Graphs with the same determinant as a complete graph Original Research Article

A family of n×n symmetric circulant (0, 1) matrices is studied. It is shown that the determinant of each matrix is (−1)n−1(n−1), a property shared with the adjacency matrix of the complete graph on n nodes. As a result, each matrix in this family generates an incomplete graph that forms a counterexample to a recent conjecture.