Ordinal Distances in Transfinite Graphs
Armen H. Zemanian · Birkhäuser Boston eBooks · 2004
The idea of distances in connected finite graphs has been quite fruitful, with much research directed toward both theory and applications. See, for example, [8], [9], [14] and the references therein. Such distances are given by a metric that assigns to each pair of nodes the minimum number of branches for all the paths connecting those two nodes. Thus, the metric takes its values in the set 1Zo if natural numbers. The objective in this chapter is to extend that metric to connected transfinite graphs and then to establish several transfinite generalizations of distance-related facts about finite graphs. This requires that our distance metric now take its values in the set R of all countable ordinals.