IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-0163-2_2.html
   My bibliography  Save this book chapter

Pristine Transfinite Graphs

In: Pristine Transfinite Graphs and Permissive Electrical Networks

Author

Listed:
  • Armen H. Zemanian

    (University at Stony Brook, Electrical Engineering Department)

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.

Suggested Citation

  • Armen H. Zemanian, 2001. "Pristine Transfinite Graphs," Springer Books, in: Pristine Transfinite Graphs and Permissive Electrical Networks, chapter 2, pages 17-28, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0163-2_2
    DOI: 10.1007/978-1-4612-0163-2_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4612-0163-2_2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.