We　performed　extensive　density-functional　calculations　to　investigate　the　stability　and　electronic　structure　of　Pd.　n　(n=　1-5)　clusters　supported　on　single　vacancy　graphene　surface,　and　adsorption　of　an　oxygen　molecule　on　such　clusters　were　studied　in　detail.　Interaction　of　the　oxygen　molecule　with　bare　Pd　cluster　was　also　calculated　for　comparison.　Our　results　show　that　point　defect　acts　as　a　strong　binding　trap　for　Pd　clusters　and　is　favorable　for　the　dispersion　of　the　Pd　nanoparticles.　Electronic　properties　analysis　shows　that　there　are　electrons　flowing　from　Pd　clusters　to　graphene.　In　addition,　the　change　of　the　DOS　for　Pd　cluster　are　mostly　attributed　to　the　hybridization　of　Pd　atoms　and　the　directly　adjacented　three　dangling　C　atoms.　Comparative　analysis　of　oxygen　molecule　adsorption　on　bare　Pd　clusters　and　graphene-supported　Pd　clusters,　the　existence　of　graphene　support　promotes　more　electrons　to　transfer　to　oxygen　molecule　and　further　makes　the　O-O　bond　elongation,　which　indicates　graphene　may　be　used　as　an　effective　support　material.　Besides,　an　energy　decomposition　scheme　is　also　employed　to　give　insight　into　the　impact　of　graphene　support　on　the　oxygen　molecule　adsorption　behavior.　©　2013　Elsevier　B.V..