Some Transfinite Graph Theory

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

Chapter 3 in Pristine Transfinite Graphs and Permissive Electrical Networks, 2001, pp 29-52 from Springer

Abstract: Abstract A peculiarity of transfinite graphs not encountered in conventional graphs is that connectedness by means of paths need not be transitive as a binary relationship between branches. In Section 3.1, we establish a criterion (Condition 3.1-2) under which transfinite connectedness through paths is transitive. The proof of this is far simpler in the present context of pristine graphs than it is for general transfinite graphs [34, Chapter 3]. Moreover, the present criterion combines the two separate ones given in [34, Conditions 3.2-1 and 3.5-1].

Keywords: Terminal Node; Finite Subset; Maximal Class; Pristine Graph; Nest Sequence (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0163-2_3

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DOI: 10.1007/978-1-4612-0163-2_3

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