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

    Bounds on the order of connected domination vertex critical graphs

    Access Status
    Fulltext not available
    Authors
    Kaemawichanurat, P.
    Caccetta, Louis
    Ananchuen, N.
    Date
    2018
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Kaemawichanurat, P. and Caccetta, L. and Ananchuen, N. 2018. Bounds on the order of connected domination vertex critical graphs. Journal of Combinatorial Mathematics and Combinatorial Computing. 107: pp. 73-96.
    Source Title
    Journal of Combinatorial Mathematics and Combinatorial Computing
    ISSN
    0835-3026
    School
    School of Electrical Engineering, Computing and Mathematical Science (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/74215
    Collection
    • Curtin Research Publications
    Abstract

    A vertex subset D of G is a dominating set of G if every vertex in V(G)-D is adjacent to a vertex in D. Moreover, a dominating set D of G is a connected dominating set if G[D] is connected. The minimum cardinality of a connected dominating set of G is called the connected domination number of G and is denoted by yc(G). A graph G is said to be fc-yc-vertex critical if yc(G) = k and yc(G-v) < k for any vertex v of G. In this paper, we establish the order of k-yc-vertex critical graphs in terms of k and the maximum degree A. We prove that a Jt-yc.-vertexcritical graph has A + k<n< (A-l)(k-l) + 3 vertices. Further, the upper bound is sharp for all integers k > 3 when A is even. It has been proved that every k-yc-vertex critical graph achieving the upper bound is A-regular for k = 2 or 3. For k = 4, we prove that every 4-yc-vertex critical graph achieving the upper bound is A-regular. We further show that, for k = 2,3 or 4, there exists a Jt-yc-vertex critical graph of order (A-l)(fc-l) + 3 if and only if A is even. We characterize, for k > 5, that every k-yc-vertex critical graph of order A + k is isomorphic to the cycle of length k + 2.

    Related items

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

    • On minimum cutsets in independent domination vertex-critical graphs
      Ananchuen, N.; Ruangthampisan, S.; Ananchuen, W.; Caccetta, Louis (2018)
      © 2018, University of Queensland. All rights reserved. Let ? i (G) denote the independent domination number of G. A graph G is said to be k-? i -vertex-critical if ? i (G) = k and for each x ? V (G), ? i (G - x) < k. ...
    • 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 ...
    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.