For　a　given　graph　F,　we　say　a　(connected)　graph　G　is　(connected)　F-saturated　if　G　is　F-free,　and　for　any　e∈E(G¯),　G+e　creates　an　F-copy.　The　(connected)　saturation　number　is　the　minimum　number　of　edges　of　a　(connected)　F-saturated　graph　with　n　vertices.　We　denote　the　saturation　number　and　the　connected　saturation　number　by　sat(n,F)　and　satc(n,F),　respectively.　Evidently,　sat(n,F)≤satc(n,F).　A　generalized　friendship　graph　is　regarded　as　the　join　of　a　clique　and　the　union　of　some　disjoint　cliques.　In　this　paper,　we　show　the　relationship　of　the　saturation　numbers　between　the　unions　of　disjoint　cliques　and　generalized　friendship　graphs,　and　as　its　application,　obtain　the　saturation　numbers　of　some　generalized　friendship　graphs.　And　then　we　propose　respectively　two　sufficient　conditions　for　sat(n,F)=satc(n,F)　and　sat(n,F)＜satc(n,F).　In　addition,　we　show　satc(n,Pk∪K3)=n+2　for　sufficiently　large　n　and　k≥4.　Furthermore,　we　obtain　an　upper　bound　of　the　saturation　number　of　Pk∪K3　for　k≥6.　©　2025