Pristine Transfinite Graphs

Armen H. Zemanian
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Armen H. Zemanian: University at Stony Brook, Electrical Engineering Department

Chapter 2 in Pristine Transfinite Graphs and Permissive Electrical Networks, 2001, pp 17-28 from Springer

Abstract: Abstract We now present explicit definitions of pristine graphs and related ideas for all ranks up to the first transfinite-ordinal rank ω; we will then indicate how the definitions can be extended to still higher ranks. The key idea is that of a “pristine node,” one that does not contain any node of lower rank. From now on, all nodes will be pristine—and therefore maximal, too; that is, no node will be contained in a node of higher rank. A transfinite graph will be called “pristine” if all its nodes are pristine. For such graphs, the definition of a transfinite path is much simpler than it is for a transfinite graph in general, and the same is true for other concomitant ideas.

Date: 2001
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DOI: 10.1007/978-1-4612-0163-2_2

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