Connectedness, Trees, and Hypergraphs

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

Chapter 3 in Graphs and Networks, 2004, pp 23-37 from Springer

Abstract: Abstract The first section, Sec. 3.1, is the more important one for this chapter. It defines the various ranks of connectedness for transfinite graphs, presents the critical Condition 3.1-2 that insures that connectedness is transitive, and shows how at each rank this partitions a transfinite graph into nonoverlapping subgraphs, called “sections.” Sec. 3.2 explains how a transfinite tree can be easily contracted to and expanded from a conventional tree. Sec. 3.3 relates the v-nodes and (y-1)-sections of a v-graph to a hypergraph and gives an example of how a result from hypergraph theory can be transferred to transfinite graph theory.

Keywords: Internal Node; Terminal Node; Boundary Node; Large Circle; Sequential Representation (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8178-4_3

Ordering information: This item can be ordered from
http://www.springer.com/9780817681784

DOI: 10.1007/978-0-8176-8178-4_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().