Backend: NetworkX 3.6.1
Python: 3.12.14
Census: alltrans16.tar / alltrans16_k=06.gz
Census text: 40 lines; 880 bytes; SHA-256 6df801e5f538cc9f406fab3e6fe1bba24744dc05b9fed7017166c6540dd8a36c
Indexing: G_i = census line i; vertex v = graph6 label v-1
All 40 graphs: simple; order16; size48; valency6; vertex-transitive; pairwise nonisomorphic
Pattern H1 = FyTAG; graph6 positions 1..n -> figure labels (2, 1, 3, 4, 5, 6, 7)
Pattern H2 = F}TJG; graph6 positions 1..n -> figure labels (2, 1, 3, 7, 6, 5, 4)
Pattern H3 = Fummw; graph6 positions 1..n -> figure labels (1, 7, 2, 6, 4, 3, 5)
Pattern H4 = G~z\z{; graph6 positions 1..n -> figure labels (1, 2, 3, 4, 5, 6, 7, 8)
Embeddings below map figure labels 1..n to census vertices in order.
H1 survivors: [20, 21, 22, 23, 24, 34, 35, 36, 37, 38, 40]
H1 embeddings: {"20": [1, 2, 6, 3, 7, 4, 5], "21": [1, 2, 6, 3, 7, 4, 5], "22": [1, 2, 6, 3, 7, 4, 5], "23": [1, 2, 5, 3, 6, 4, 7], "24": [1, 2, 5, 3, 6, 4, 7], "34": [1, 2, 5, 3, 7, 4, 6], "35": [1, 2, 4, 3, 5, 6, 7], "36": [1, 2, 3, 4, 7, 5, 6], "37": [1, 2, 3, 4, 7, 5, 6], "38": [1, 2, 3, 4, 7, 5, 6], "40": [1, 2, 3, 4, 6, 5, 7]}
H2 induced embeddings: {"34": [1, 2, 5, 7, 3, 4, 6], "36": [1, 2, 3, 7, 4, 5, 6], "37": [1, 2, 3, 7, 4, 5, 6], "38": [1, 2, 3, 6, 5, 7, 4]}
After H2: [20, 21, 22, 23, 24, 35, 40]
G20 centre=1 closed=[1, 2, 3, 4, 5, 6, 7]; degree_1(2)=2; edge=(2,6); forced=(1, 2, 6)
G20 closed-neighbourhood edges at 1: [(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 6), (3, 7), (4, 5), (4, 7), (5, 7), (6, 7)]
G20 centre=6 closed=[1, 2, 6, 7, 12, 14, 16]; degree_6(7)=2; edge=(7,1); forced=(1, 6, 7)
G20 closed-neighbourhood edges at 6: [(1, 2), (1, 6), (1, 7), (2, 6), (2, 12), (2, 14), (2, 16), (6, 7), (6, 12), (6, 14), (6, 16), (14, 16)]
G21 centre=1 closed=[1, 2, 3, 4, 5, 6, 7]; degree_1(2)=2; edge=(2,6); forced=(1, 2, 6)
G21 closed-neighbourhood edges at 1: [(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 6), (3, 7), (4, 5), (4, 7), (5, 7), (6, 7)]
G21 centre=6 closed=[1, 2, 6, 7, 13, 14, 16]; degree_6(7)=2; edge=(7,1); forced=(1, 6, 7)
G21 closed-neighbourhood edges at 6: [(1, 2), (1, 6), (1, 7), (2, 6), (2, 13), (2, 14), (2, 16), (6, 7), (6, 13), (6, 14), (6, 16), (14, 16)]
G22 centre=1 closed=[1, 2, 3, 4, 5, 6, 7]; degree_1(2)=2; edge=(2,6); forced=(1, 2, 6)
G22 closed-neighbourhood edges at 1: [(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 6), (3, 7), (4, 5), (4, 7), (5, 6), (6, 7)]
G22 centre=6 closed=[1, 2, 5, 6, 7, 11, 15]; degree_6(7)=2; edge=(7,1); forced=(1, 6, 7)
G22 closed-neighbourhood edges at 6: [(1, 2), (1, 5), (1, 6), (1, 7), (2, 6), (2, 11), (2, 15), (5, 6), (5, 15), (6, 7), (6, 11), (6, 15)]
G23 centre=1 closed=[1, 2, 3, 4, 5, 6, 7]; degree_1(3)=2; edge=(3,6); forced=(1, 3, 6)
G23 closed-neighbourhood edges at 1: [(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 5), (3, 6), (4, 6), (4, 7), (5, 7), (6, 7)]
G23 centre=6 closed=[1, 3, 4, 6, 7, 12, 16]; degree_6(12)=2; edge=(12,3); forced=(3, 6, 12)
G23 closed-neighbourhood edges at 6: [(1, 3), (1, 4), (1, 6), (1, 7), (3, 6), (3, 12), (4, 6), (4, 7), (4, 16), (6, 7), (6, 12), (6, 16)]
G24 centre=1 closed=[1, 2, 3, 4, 5, 6, 7]; degree_1(3)=2; edge=(3,6); forced=(1, 3, 6)
G24 closed-neighbourhood edges at 1: [(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 5), (3, 6), (4, 6), (4, 7), (5, 7), (6, 7)]
G24 centre=6 closed=[1, 3, 4, 6, 7, 12, 16]; degree_6(12)=2; edge=(12,3); forced=(3, 6, 12)
G24 closed-neighbourhood edges at 6: [(1, 3), (1, 4), (1, 6), (1, 7), (3, 6), (3, 12), (4, 6), (4, 7), (4, 16), (6, 7), (6, 12), (6, 16)]
After local tests: [35, 40]
G35 H3 induced embedding: (1, 2, 4, 6, 7, 5, 3)
G40 H4 induced embedding: (1, 2, 3, 4, 5, 6, 7, 16)
G40 equal open neighbourhoods: 1 and 16 -> [2, 3, 4, 5, 6, 7]
Remaining graphs: []
ALL ASSERTIONS PASSED
