With　the　rapid　expansion　of　the　scale　of　multiprocessor　systems,　the　importance　of　fault　tolerance　and　fault　diagnosis　is　increasingly　concerned.　For　an　interconnection　network　G,　the　h-component　connectivity　is　an　important　indicator　for　evaluating　the　fault　tolerance　of　G,　which　is　defined　as　the　minimum　number　of　vertices　whose　deletion　will　disconnect　G　such　that　the　remaining　has　at　least　h　components.　The　h-component　diagnosability,　a　newly　precise　diagnosis　strategy　to　analyze　the　reliability　of　G,　is　the　diagnosability　under　the　condition　that　the　number　of　components　is　at　least　h　in　the　resulting　graph　after　removing　the　faulty　processor　set.　The　t/k-diagnosability　is　a　classic　imprecise　diagnosis　strategy,　which　can　identify　up　to　t　faulty　processors　by　sacrificing　accuracy　to　a　certain　extent,　namely　misdiagnosing　at　most　k　fault-free　processors.　In　this　paper,　we　investigate　some　combinatorial　properties　and　the　fault　tolerance　ability　of　the　n-dimensional　Bicube　network,　denoted　by　BQ(n).　Then　we　first　prove　that　the　(h　+　1)-component　connectivity　of　BQ(n)　is　h(n　-1)　-　h(h-1)/2　+　1　(n　＞=　6,　1　＜=　h　＜=　n　-　1).　Moreover,　we　derive　that　the　(h　+　1)-component　diagnosability　of　BQ(n)　is　(h　+1)(n-1)　-　h(h+1)/2　+　1　under　the　PMC　model　and　MM*　model　(n　＞=　7,　1　＜=　h　＜=　n-3).　Furthermore,　under　the　PMC　model,　we　propose　the　t/k-diagnosis　algorithm　of　BQ(n)　and　then　derive　that　BQ(n)　is　[(k　+1)n　-　k(k+3)/2]/k　diagnosable　(n　＞=　6,　0　＜=　k　＜=　n　-　2)　(C)　2021　Elsevier　B.V.　All　rights　reserved.