On 2-rainbow domination in generalized Petersen graphs

摘要

In this paper, we show that γ_(r2)(GP(n,k)) ≤ n - 1 for all n ≥ 13 except n = 2k+2, where GP(n, k) is a generalized Petersen graph and γ_(r2)(GP(n, k)) is the 2-rainbow domination number of GP(n,k). We also conjecture that γ_(r2)(GP(n,k)) = n if and only if k= 1, or n = 2k+2 for k ≥ 3, or (n,k) _∈ {(5,2), (7,2), (7,3), (10,3), (11,3), (11,4)}.