{"schema_version":"ocme-site-results-v1","locale":"zh-Hant","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-graph-isomorphism"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-graph-isomorphism-01","title":{"zh-Hant":"圖同構：以完整映射表逐項核對雙射與鄰接當且僅當","en":"Graph isomorphism: checking bijectivity and both directions of adjacency preservation from a complete mapping table"},"summary":{"zh-Hant":"G 的頂點為 1、2、3、4，邊為 {1,2}、{2,3}、{3,4}、{1,4}；H 的頂點為 a、b、c、d，邊為 {a,c}、{b,c}、{b,d}、{a,d}。證明映射 f：1↦a、2↦c、3↦b、4↦d 是圖同構 G→H；說明雙射 g：1↦a、2↦b、3↦c、4↦d 不是同構；並證明路徑 P（邊 {1,2}、{2,3}、{3,4}）與 H 不同構，即使 f 把 P 的每條邊都送到 H 的邊。","en":"G has vertices 1, 2, 3, 4 and edges {1,2}, {2,3}, {3,4}, {1,4}; H has vertices a, b, c, d and edges {a,c}, {b,c}, {b,d}, {a,d}. Prove that f: 1↦a, 2↦c, 3↦b, 4↦d is a graph isomorphism G→H; show that the bijection g: 1↦a, 2↦b, 3↦c, 4↦d is not an isomorphism; and prove that the path P (edges {1,2}, {2,3}, {3,4}) is not isomorphic to H, even though f sends every edge of P to an edge of H."},"mko_ids":["mko-graph-isomorphism"]}],"title":"概念推導導讀"}