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论文类型：期刊论文

发表时间：2012-07-01

发表刊物：UTILITAS MATHEMATICA

收录刊物：SCIE、Scopus

卷号：88

页面范围：317-335

ISSN号：0315-3681

关键字：Domination; Liar's domination number; Generalized Petersen Graph

摘要：A set L subset of V(G) is a liar's dominating set if and only if L is a double dominating set and vertical bar(N[u] boolean OR N[v]) boolean AND L vertical bar >= 3 for every pair u and v of distinct vertices in G. The minimum cardinality of a liar's dominating set for graph G is the liar's domination number of G, denoted by gamma LR(C). In this paper, we study the liar's domination number of generalized Petersen graphs P(n, 1) and P(n, 2). We prove that for n >= 3,
   gamma LR(P(n,1))= (7n/6]
   and for n >= 5,
   11(41+1 gamma LR(P(n, 2)) = {[10n/9] +1 n equivalent to 8 (mod 9) [10n/p] n not equivalent to 8 (mod 9).