Inverse of the distance matrix of a cactoid digraph

Abstract A strongly connected directed graph in which any two directed cycles of it share at most one common vertex is called a cactoid digraph. Let D be its distance matrix. By a theorem of Graham, Hoffman and Hosoya, we have det ⁡ ( D ) ≠ 0 . In this paper, we give the formulas for both the determinant and the inverse of the distance matrix D for a cactoid digraph.