Objects, Invariants and Properties for Graph Theory (GT) automated conjecturing: in particular with the Sage program CONJECTURING: http://nvcleemp.github.io/conjecturing/
From:
Goddard, Wayne, and Ortrud R. Oellermann. "Distance in graphs." In Structural Analysis of Complex Networks, pp. 49-72. Birkhäuser Boston, 2011.
(1) the status of a vertex v (in a connected graph) is the sum of distances from v to all other vertices,
(2) and the minimum_status of a (connected) graph is the minimum status of its vertices.
From: Goddard, Wayne, and Ortrud R. Oellermann. "Distance in graphs." In Structural Analysis of Complex Networks, pp. 49-72. Birkhäuser Boston, 2011.
(1) the status of a vertex v (in a connected graph) is the sum of distances from v to all other vertices, (2) and the minimum_status of a (connected) graph is the minimum status of its vertices.