On the distance matrix of a directed graph

Abstract

In this note, we show how the determinant of the distance matrix D(G) of a weighted, directed graph G can be explicitly expressed in terms of the corresponding determinants for the (strong) blocks Gi of G. In particular, when cof D(G), the sum of the cofactors of D(G), does not vanish, we have the very attractive formula (Formula Presented.) . Copyright © 1977 Wiley Periodicals, Inc., A Wiley Company