Inverse of the distance matrix of a weighted cactoid digraph

摘要

A weighted cactoid digraph is a strongly connected directed graph whose blocks are weighted directed cycles such that any two distinct weighted directed cycles of this graph share at most one common vertex. In this paper, we give the determinant and the inverse of the distance matrix of a weighted cactoid digraph, which imply Graham and Pollak’s formula and the inverse of the distance matrix of a tree.