IDEAS home Printed from https://ideas.repec.org/a/sae/envirb/v5y1978i1p31-43.html
   My bibliography  Save this article

On Enumerating Certain Design Problems in Terms of Bicoloured Graphs with No Isolates

Author

Listed:
  • F Harary

    (Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA)

  • L March

    (Design Discipline, Faculty of Technology, The Open University, Milton Keynes MK7 6AA, England)

  • R W Robinson

    (Department of Mathematics, University of Newcastle, New South Wales, Australia, 2308)

Abstract

The enumeration of zero-one matrices with nonzero row and column sums has recently been solved in the context of certain problems arising in architectural design. However, this solution took no account of the symmetries of these configurations, which would be required for any realistic application in an architectural context. In graph-theoretic terms, this new problem calls for counting unlabelled bicoloured graphs with no isolated points. We determine these numbers by deriving their generating function. We also present an equivalent set of recurrence relations, from which the numbers may be easily computed.

Suggested Citation

  • F Harary & L March & R W Robinson, 1978. "On Enumerating Certain Design Problems in Terms of Bicoloured Graphs with No Isolates," Environment and Planning B, , vol. 5(1), pages 31-43, June.
    • Handle: RePEc:sae:envirb:v:5:y:1978:i:1:p:31-43
    DOI: 10.1068/b050031
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1068/b050031
    Download Restriction: no
    File URL: https://libkey.io/10.1068/b050031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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:sae:envirb:v:5:y:1978:i:1:p:31-43. 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: SAGE Publications (email available below). General contact details of provider: .

    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.