Realizing the distance matrix of a graph

Abstract

An explicit description is give n for the unique graph with as few arcs (eac h bearing a positive length) as possible, whi ch has a prescribed matrix of shortest-path distan ces be tween pa irs of distinct vertices. The same is done in the case when the ith diagonal matrix e ntry, in stead of be ing zero, represents the. length of a s hort est closed path containing the ith vertex