Some graph invariants related to the distance matrix of a digraph

Abstract

It is the very usual case that the sbortest paths between all pairs of vertices in a given graph are required. Then the distance matrix D of such graph has to be arranged. In addition some quantities related to the distance matrix D can be useful. The program in the system Mathematica was created to calculate specific quantities for a given directed graph. Further the determinant of the distance matrix and the distance polynomial for a cycle with n vertices were found.