Liar's Domination Number of Generalized Petersen Graphs P(n, 1) and P(n, 2)

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).