Curtin University Homepage
  • Library
  • Help
    • Admin

    espace - Curtin’s institutional repository

    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item

    Cubic and quadruple Paley graphs with the n-e.c. property

    Access Status
    Fulltext not available
    Authors
    Ananchuen, Watcharaphong
    Caccetta, Louis
    Date
    2006
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Ananchuen, W. and Caccetta, L. 2006. Cubic and quadruple Paley graphs with the n-e.c. property. Discrete Mathematics. 306 (22): pp. 2954-2961.
    Source Title
    Discrete Mathematics
    Additional URLs
    http://www.elsevier.com/wps/find/journaldescription.cws_home/505610/description#description
    ISSN
    0012365X
    URI
    http://hdl.handle.net/20.500.11937/17637
    Collection
    • Curtin Research Publications
    Abstract

    A graph G is n-existentially closed or n-e.c. if for any two disjoint subsets A and B of vertices of G with |A ∪ B| = n, there is a vertex u /∈A ∪ B that is adjacent to every vertex of A but not adjacent to any vertex of B. It is well-known that almost all graphs are n-e.c. However, few classes of n-e.c. graphs have been constructed. A good construction is the Paley graphs which are defined as follows. Let q ≡ 1(mod 4) be a prime power. The vertices of Paley graphs are the elements of the finite field Fq. Two vertices a and b are adjacent if and only if their difference is a quadratic residue. Previous results established that Paley graphs are n-e.c. for sufficiently large q. By using higher order residues on finite fields we can generate other classes of graphs which we called cubic and quadruple Paley graphs. We show that cubic Paley graphs are n-e.c. whenever q_n224n−2 and quadruple Paley graphs are n-e.c. whenever q_9n262n−2.We also investigate a similar adjacency property for quadruple Paley digraphs.

    Related items

    Showing items related by title, author, creator and subject.

    • Graphs with prescribed adjacency properties
      Ananchuen, Watcharaphong (1993)
      A graph G is said to have property P(m,n,k) if for any set of m + n distinct vertices there are at least k other vertices, each of which is adjacent to the first m vertices but not adjacent to any of the latter n vertices. ...
    • Graphs that are critical with respect to matching extension and diameter
      Ananchuen, Nawarat (1994)
      Let G be a simple connected graph on 2n vertices with a perfect matching. For 1 ≤ k ≤ n - 1, G is said to be k-extendable if for every matching M of size k in G there is a perfect matching in G containing all the edges ...
    • A characterization of 3-i-critical graphs of connectivity two
      Ananchuen, N.; Ananchuen, W.; Caccetta, Louis (2017)
      A subset S of V (G) is an independent dominating set of G if S is independent and each vertex of G is either in S or adjacent to some vertex of S. Let i(G) denote the minimum cardinality of an independent dominating set ...
    Advanced search

    Browse

    Communities & CollectionsIssue DateAuthorTitleSubjectDocument TypeThis CollectionIssue DateAuthorTitleSubjectDocument Type

    My Account

    Admin

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Follow Curtin

    • 
    • 
    • 
    • 
    • 

    CRICOS Provider Code: 00301JABN: 99 143 842 569TEQSA: PRV12158

    Copyright | Disclaimer | Privacy statement | Accessibility

    Curtin would like to pay respect to the Aboriginal and Torres Strait Islander members of our community by acknowledging the traditional owners of the land on which the Perth campus is located, the Whadjuk people of the Nyungar Nation; and on our Kalgoorlie campus, the Wongutha people of the North-Eastern Goldfields.