On the minors of an incidence matrix and Smith normal form
The possible minors of a vertex-edge incidence matrix of an undirected loopless graph are completely determined. Then the maximum and minimum absolute values of the maximal minors of the incidence matrix as well as its Smith normal form are determined. The results are used to obtain a sufficient condition for a system of equations (whose coefficient matrix is an incidence matrix) to admit an integer solution.
scientific article; zbMATH DE number 753870
scientific article