NAME

Xu Xirong

Paper Publications

On the Distance Paired-Domination of Circulant Graphs
  • Hits:
  • Indexed by:

    期刊论文

  • First Author:

    Wang, Haoli

  • Correspondence Author:

    Wang, HL (reprint author), Dalian Univ Technol, Dept Comp Sci, Dalian 116024, Peoples R China.

  • Co-author:

    Xu, Xirong,Yang, Yuansheng,Wang, Guoqing,Lue, Kai

  • Date of Publication:

    2011-01-01

  • Journal:

    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY

  • Included Journals:

    Scopus、SCIE

  • Document Type:

    J

  • Volume:

    34

  • Issue:

    1

  • Page Number:

    1-19

  • ISSN No.:

    0126-6705

  • Key Words:

    Paired-domination number; d-distance paired-domination number; circulant graph

  • Abstract:

    Let G = (V, E) be a graph without isolated vertices. A set D C V is a d-distance paired-dominating set of G if D is a d-distance dominating set of G and the induced subgraph (D) has a perfect matching. The minimum cardinality of a d-distance paired-dominating set for graph G is the d-distance paired-domination number, denoted by gamma(d)(p)(G). In this paper, we study the d-distance paired-domination number of circulant graphs C(n; {1, k}) for 2 <= k <= 4. We prove that for k = 2, n >= 5 and d >= 1,
       gamma(p)(d) (C(n; {1, k})) = 2 inverted right perpendicular n/2kd + 3 inverted left perpendicular,
       for k = 3, n >= 7 and d >= 1,
       gamma C-d((p)(n; {1, k})) = 2 inverted right perpendicular n/2kd + 2 left perpendicular,
       and for k = 4 and n >= 9,
       (i) if d = 1, then
       gamma p(C(n; {1, k})) ={ 2 inverted right perpendicular 3n/23 inverted left perpendicular + 2, if n  15,22 (mod 23); 2inverted right perpendicular2n/4kd+1inverted left perpendicular,
       otherwise gamma(p)(d)(C(n; {1, k})) = { 2inverted right perpendicular 2n/4kd+1inverted left perpendicular + 2, if n  2kd, 4kd - 1, 4kd (mod 4kd + 1) 2inverted right perpendicular 2n/4kd + 1inverted left perpendicular, otherwise.

Pre One:An important property about vertex distance of Crossed Cubes CQn

Next One:On infinite families of optimal double-loop networks with non-unit steps