Connectedness

Armen H. Zemanian
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Armen H. Zemanian: State University of New York at Stony Brook, Department of Electrical Engineering

Chapter Chapter 3 in Transfiniteness, 1996, pp 47-78 from Springer

Abstract: Abstract A key difference between conventional infinite graphs and transfinite graphs is that in conventional graphs two nodes are either connected through a finite path (i.e., a path of finitely many branches) or not connected at all, whereas in transfinite graphs two nodes may be connected through a transfinite path (i.e., one having infinitely many branches) but not through any finite path. In fact, for transfinite graphs there is a hierarchy of connectedness concepts, which is indexed by the countable ordinals. Thus, we speak of two nodes being “ρ-connected” when the two nodes are connected through a two-ended α -path for some α no larger than ρ. As ρ increases,ρ- connectedness weakens in the sense that, when ρ1

Keywords: Natural Number; Boundary Node; Infinite Sequence; Minimum Rank; Maximal Node (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0767-2_3

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DOI: 10.1007/978-1-4612-0767-2_3

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