A formula for all minors of the adjacency matrix and an application

Abstract

We supply a combinatorial description of any minor of the adjacency matrix of a graph. This descriptionis then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of agraph G, whenever A(G) is invertible, where G is formed by replacing the edges of a tree by path bundles.

Keywords

• adjacency matrix
• linear subgraphs
• minors
• path bundle
• 05c50
• 05c05
• 15a18