Resumen de Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

Jozef Kratica, Dragan Matic, Vladimir Filipovic

• We consider the weakly convex and convex domination numbers for two classes of graphs: generalized Petersen graphs and flower snark graphs. For a given generalized Petersen graph GP(n, k), we prove that if k = 1 and n ≥ 4 then both the weakly convex domination number γwcon(GP(n, k)) and the convex domination number γcon(GP(n, k)) are equal to n. For k ≥ 2 and n ≥ 13, γwcon(GP(n, k)) = γcon(GP(n, k)) = 2n, which is the order of GP(n, k). Special cases for smaller graphs are solved by the exact method. For a flower snark graph Jn, where n is odd and n ≥ 5, we prove that γwcon(Jn) =2n and γcon(Jn) = 4n.