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Ordinal Distances in Transfinite Graphs,ample, [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

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Walk-Based Transfinite Graphs and Networks,xtremities of the graph are specified through equivalence classes of one-ended paths. This is a natural extension of finite graphs because connectedness for finite graphs is fully characterized by paths; indeed, any walk terminating at two nodes of a finite graph contains a path doing the same. Howe

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Hyperreal Transients in Transfinite RLC Networks,ks. That is, the branch parameters have only been (linear or nonlinear) resistors along with voltage and current sources. However, the technique employed in Chapter 6, whereby the transfinite network N. is viewed as the end result of a sequence of finite networks that fill out N., now makes it possi

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Transfinite Graphs,as been discussed at some length in [51] along with a variety of illustrative examples.’ Our purpose here is to provide enough information to relieve the reader from any need to consult that prior work.

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Hyperreal Currents and Voltages in Transfinite Networks,

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Mutationstheorie der Geschwulst-Entstehung 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.