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Indexed by:期刊论文

Date of Publication:2011-01-01

Journal:BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY

Included Journals:Scopus、SCIE

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.