Add a list of graphs we found

graph_list.py

+"""List of examples that Z_4- and Z_2^2-connectivity are different notions.
+"""
+
+def cube_4y():
+  """The 2 nonisomorphic subdivisions of cube which are Z_4- but not
+  Z_2^2-connected.
+
+  There is no subdivison of cube with the group connectivity the other way
+  around.
+  """
+
+  return ['J?EQX_g_Q@_', 'J?CSZ`GHC@_']
+
+
+# There is no graphs10_4n because we did not found any such graphs.
+
+def graphs10_4y():
+  """List graphs which are Z_4- but not Z_2^2-connected.
+
+  It contains 35 nonisomorphic graphs on 15 verices (3-fold
+  subdivisons of 10-vertex cubic graphs) encoded as graph6
+  strings.
+  """
+  
+  return [
+    'L@FEBO__G_`_?g', 'LCMER@C@P??DCC', 'LDObGADAS?gGE?', 'LCSbGAD_QAE?AC',
+    'LCIER?cDA@B??S', 'LDS`IA@aAC?c?S', 'LDObGADaAAB??S', 'LDSb?AD_QA@A@_',
+    'LoOSH`?I_o?c?W', 'L?MER@?DS_CC@G', 'L@FE@OacAA@_?K', 'LDS`IAC_QC@A?W',
+    'LCSbGACaQAE??W', 'LoSCH@DG_gAGAC', 'L@FMAO__HAAA?g', 'LDSbAADa?G?P?S',
+    'LDObGA@aQAB?@G', 'LDCbGADAS?h?OO', 'LCObGADaQAE?E?', 'LCEEP@_DQAD?@G',
+    'LDS`IAD_AC@A?S', 'LCIEQ@cD@AB??S', 'LAp`?ABKS_@G@_', 'LCIEP@_DQAB?@G',
+    'LCEER?cDA@D??S', 'LoOS@`CI_o?o?W', 'LCMER@CCP??D@C', 'L@FMB?ac?Q?C?D',
+    'LCIAR@cCSCB?@C', 'LCMER?_@Q@AA@G', 'LCMEA@cD@A@O?S', 'LDSBIACa@G?K?S',
+    'LCMER@?@P@AA@G', 'LoCS@`CIaO?o?W', 'L?MER@CCS_CC@C'
+  ]
+
+def graphs12_4n():
+  """List graphs which are Z_2^2- but not Z_4-connected.
+
+  It contains 7 nonisomorphic graphs on 15 verices (3-fold
+  subdivisons of 12-vertex cubic graphs) encoded as graph6
+  strings.
+  """
+
+  return [
+    'NHQ?_E_OOOb__A@O?S?',
+    'NKE?GP@G__x?H??g?H?',
+    'NKC_GOBG_Ax?`?OGA@?',
+    'NKE_G@@G_Ax?CAAO?S?',
+    'NKE_G?BG_Ax?OGCA@G?',
+    'N?_cC_aOooGcQ?GAA_?',
+    'N@OAcIG_@B?qS?GC@_?'
+  ]
+
+
+def graphs12_4y():
+  """List graphs which are Z_4- but not Z_2^2-connected.
+
+  It contains 619 nonisomorphic graphs on 15 verices (3-fold
+  subdivisons of 12-vertex cubic graphs) encoded as graph6
+  strings.
+  """
+
+  return [
+    'NB_GTG_O?DoAP?C@?S?', 'N`@`OGP?WoPA_??AgO?', 'N_@bOGP?[o@?_@K??A_', 'NBOIcIGg?@?aGA?`?H?',
+    'NQ@?oY_?WGCB__Q?A@?', 'NBGe??@aGMOCO@D?@G?', 'NQ?CoW_?WgCB_GQ?G_?', 'NHQ?_MaOC?b?AA@@?I?',
+    'NCA_GP@G_ax?W?E??S?', 'NRO?AGCAgIQO_GI??P?', 'N@@bOG@?[o@Ao?_@AC?', 'NKLH?H?_S_?U?a?O?CG',
+    'NHQ?_E?OSOb_GG@O?S?', 'NQ?CoY_?GgCBQ?P??I?', 'N@W?AICAgKQOg?S??H?', 'N`@b?GP?KOPACAA_?I?',
+    'NHQ?_M_OSOA_A@?g?B?', 'N?DpOAA_OBW@Q?GOAA?', 'NRW?AI??gMQ?AC@G?O_', 'NQ@CoY??Wg?BQ?GGC?_',
+    'NHQ?_MaOC?`_C@AA?I?', 'NRG?AGCA_MQO_GQ??E?', 'N?T@PAAcOBW?H?D??@_', 'NAU?CCCGk_CDO_I??g?',
+    'NBW?AIC?gIQOg?AC?P?', 'NAOI_I?g@B?q_OK?@C?', 'NA]ACK??k_?DGCG@?c?', 'NGA?_IaOSOb_Q?K??W?',
+    'NKE_GP@G_aH?_@?g?B?', 'NCA?Q@E[CI@GG_G@B??', 'NCE@Q@E[CAC?A@@A?G_', 'N?TpPAAc?AW@?S?G?@G',
+    'N`@b?G@?[_PACGA_@@?', 'NCE@A@ESCICGGCA_@?_', 'NCE@O?ESCIDGOOOGCA?', 'NKA_GPAG_ap?O@E??K?',
+    'NKLH?@@_SC?QCA@O?C_', 'N?E@A@E[CICGc?A_@?_', 'NCJ_QC@C@O?U_GOCA@?', 'NBGs?O?aGEWCO_@A?K?',
+    'N`@b?GP?[O@A_@CA@O?', 'NRW?AIC?_MAO_@AC?E?', 'N?@bOGP?[oOAo?K?@?_', 'NA]ACGCGk_C??o?H?@_',
+    'N@Gu?O@_GMW?S?AC?C_', 'N@OIcIG_@@?qS?GC?H?', 'N`?bOGP?[OOAP?CA@?_', 'NKE?GPBG__p?O@H??H?',
+    'NIQSOCp@@??B_@AO?B?', 'N?Tp?AAcOBW?GOA_?@_', 'NKE?GPBG_Ap?O@H?A@?', 'N?ooC_A?poGc__OCCC?',
+    'NB_GTGAO?DoAP?GGA?_', 'NRW?AACAgEAO_@@O?`?', 'NHQ?_EaOSOB?@O@@?B?', 'NQG?AI?AgMQOQ?K??c?',
+    'N`@bOG@?WoPA_??AaC?', 'NQOCoQ_?OgCBP?@O?E?', 'NBW?AICAgIQ?g??a?O_', 'NKE_GPBG?AX?CA?c?B?',
+    'NBGs?O?aGMGC_@O_?K?', 'NGQ?_IaOS?b_K?AA?W?', 'NKE_G@BG?aX?AO?c?B?', 'NRO?AI?AgKQOI?@G?H?',
+    'NCE@Q@EW?ID?_ACC?G_', 'N@B?U_IGICCA_@CA@_?', 'NHQ??MaOCOB_C_?S?B?', 'NSSH@?O@[??hO_OG?P?',
+    'NKE_?@BG_aw?AOA@?o?', 'NHQ?_MaOCOa?A@@@?I?', 'NCE@Q@C[CACGA@@A?S?', 'N?ocC_A?poGcOCGGA_?',
+    'N?TpOA?cOAW@GO?g?D?', 'N?osC_aO_oGCGA@@?I?', 'NKDH?H@_SC?QI?CA?C_', 'N`?bOGO?[o@A_@P??K?',
+    'NCJ_QC@C@o?E_GOC?O_', 'NBW?AICAGMQOg??_?AG', 'NSS@@@?@[C?hO_CG@_?', 'NQ@CoW_?W_CB_GQ??`?',
+    'N`@aOGP?WoPA_??AcO?', 'NKE_?OBG_Ax?OGCA?o?', 'N?DPPAAc?BW@Q?H??I?', 'NAGs?O?aGMWCO_K??K?',
+    'NHQ?_E_OSO`_C@@O?S?', 'NCH?OE@S@o?U`?OOC_?', 'N`@aOGP?[O@A_@G_A@?', 'N@@bOGP?[OOAo?CA@?_',
+    'NODKa@?@HAaC_OG_@?_', 'N?osC_a?ooG_OCGA?C_', 'NPO?AICAgMAO_@S?D??', 'N_@bOGP?[oO?K?A@?A_',
+    'NCC_GPBG_Ax?`?W?A@?', 'N@@bO?P?[o@Ao?_@?g?', 'N_@`O?P?[oPAO_K??g?', 'N`@bOG@?[oOACGA???g',
+    'N`@aOGP?SOPAG_CA?E?', 'NHQ??MaOS?b?C_AA?__', 'NB`GDGa??Dq?OCA_?A_', 'NKE?GP@G_Ax?H?CA?S?',
+    'NRW??ACAgMOOOOC@?g?', 'NC?XV?OOC@cAQ?@@?S?', 'N[CCOCDGIO?`O@CC?g?', 'NA]?CGCGk_CCO_?o?@_',
+    'NKL??H@_Sc?QG_B??C_', 'N@@aOGP?WoPAo?_ACO?', 'N?_cC_aOpoGcO?A?a_?', 'NCOXV?OOC@_AG@@@?S?',
+    'NQOCoI_?OgCBP?AO?E?', 'NCJ?QC@O@o?U_GH?AA?', 'NRW??ICAgEOOOOC@?`?', 'N@@aOGP?[o@Ao?_@CO?',
+    'NC@_QC@S@o?U`?_GD??', 'NRG?A?CAgMQO_GQ??g?', 'N?E@O?E[CIDGc?OOGC?', 'N?osC_aOOoGcGA?_?AG',
+    'NA]ACK?Gk??DG@CA?c?', 'N@OIcIGg?@?qS?GA?H?', 'N?osC_aOOo?cO@GA?Q?', 'N[C?OKDGGOG`__OAAA?',
+    'NB?IcAGg@@?qQ?@O?H?', 'NRO??ICAgIQOOOI??P?', 'NCJ_AE@C@o?QOCA_?C_', 'N`@b?GP?WoP?_AA_?A_',
+    'NKE?GPAG_ax?G?@?_K?', 'NQW?AICAgKAO_@K??H?', 'N?osC_aO`oG_?O?C_C_', 'NGA?_MaOSOb?Q?K??__',
+    'NHQ?_EaOSO@_C@@O?B?', 'NAYACCCGk_C@E?@O?C_', 'NQ@CoQ_?WGCBQ?CA?g?', 'N@BGE?IGGcSAOACO@O?',
+    'NBGu??@a?MOCO@AO?E?', 'NRG?AACAgMAO_@Q??g?', 'N?PoPAA_OBW@G_E?AA?', 'NQOC_W_?WgCB_GP?@O?',
+    'N?PpP??cOBW@_GE??S?', 'N?osC_a?`OGcOCCA?I?', 'N?PpPA?_OBW@E?CC?S?', 'N@@BOGP?WoPAo?_AC_?',
+    'NCH_AE@C@o?U`?OC@O?', 'NKE_?P@G_aw?A@@_?S?', 'NRW?AICAgAOOC@@A?P?', 'N@Q?_MAOSOB_W?GG?B?',
+    'N?osC__?poGCOC@@?S?', 'N?PpPA?cO@W@E??g?H?', 'NA]ACGC?k_C@GC?o?C_', 'N?osC__Op_GCAA@@?S?',
+    'NKDH?G@_SC?UOGI?A@?', 'NCHH?H@_Sc?EW?E??O_', 'N@BGU?IGA_SACO?a?E?', 'N?TpPA?c?BW??g?S?@_',
+    'NQ@COW_?WgCB_GQ?AO?', 'NKE_GPBG?aW?A@?c?B?', 'N?PpPAAcO@O@O@E??H?', 'N?osC__O`oG_?g?S?C_',
+    'NBGU?O@_GIWCH?AC?P?', 'NKE_GOBG__h?_@OG?H?', 'NS??K?eS?Qh_W?C_@G?', 'NB?I_AGg@B?q_OQ??g?',
+    'NHA?_CaOSOb__GQ??g?', 'NQOC?Y_?WgCBP?C_@O?', 'N?osC?aO`o?cO@CO?I?', 'NBW?AIC?_MQOg?AC?E?',
+    'NA]ACK?GK_?DG@@G?Q?', 'NCE@Q@EKCADGOC@??@G', 'N_AOBOIa?DE@W?CC?o?', 'N?o_C_a?poGc__OCA_?',
+    'NCH_QA@S?o?U`?GA?W?', 'NBOICIGg?@?qGAC_?H?', 'N?ocC_aOPo?cO@D??Q?', 'NAYACKCGk_C@C?A?_C_',
+    'NKLG?@@_Sc?QG_@O?C_', 'NQ@?oQ_?WgCB__Q??g?', 'N@`GTG_O?DoAS?C@?S?', 'NKE?GPBG__x?H??O?@G',
+    'NKHH?@@_Sc?EE?@O?O_', 'NKL@?G@_Sc?EOGB??O_', 'NRW??ICA_MQ?OO?`?E?', 'N?osC__O`_GcAA?g?I?',
+    'NRW??ACAgMAO_@OO?g?', 'NQ@COY_?Wg?BQ?G@AO?', 'NGQ?_MAOSO`_K?GGA?_', 'NPW?AICAGMQOS??_?AG',
+    'N?DpPAAcOBO?Q?O@?@_', 'NQOCoW_?WGCB_GP?A@?', 'NRO??I?AgMQOOOI??c?', 'N?TpPAA_OAW@CC?G?@G',
+    'NHQ??MaOCOb_C??__I?', 'NHQ?_Ma?CO`_OCC@?I?', 'NHQ?_MAOCOb?GG@@?I?', 'NKE_?P@G_ap?O@@_?S?',
+    'N@`GTGaO?DOAS?C@?B?', 'NSOJ@@O@S??hE??a?E?', 'NBOIcI?G@@?q_CAG?H?', 'NQW?AI?AgMAO_@K??c?',
+    'N`@BOGP?[oO?H?A@?A_', 'NA]ACKCGK_?@G@?c?C_', 'N?PpPAACOBO@_CO@B??', 'NKE_GPBG?_x??c?O?@G',
+    'N`@bO?P?[?PACAAA?g?', 'NBOICAGg@A?qC_@O?D?', 'NHQ?_EaOS?`_C@AA?g?', 'NHA?_MaOCOb?Q?@@?I?',
+    'NHQ?_CaOSOa__GA@?g?', 'N`@aOGP?[?PAG_CA@@?', 'N`?aOG@?[oPAP?G_AC?', 'N`?bOGP?[o@?_@P??A_',
+    'NHQ?_E_OSOb_@??O_S?', 'N@OIcAGg@@?qS?@O?H?', 'N?E@Q?E[CID?c?OG?G_', 'NQOCoY_?GgCAP??S?@_',
+    'NBGu??@aGEW?AO@A?C_', 'N@OI_IGg@B?q_??Oi??', 'N?Q?_MaOSOB_W?K??B?', 'NBOICAGg@@?qC_@O?H?',
+    'NKLH?G@_CC?UOGCA?I?', 'NBOAcIGg?A?qGAB??D?', 'NRW?AI??gMOOC@AC?c?', 'NKLH?H?_S_?U?_?A_K?',
+    'NCJ_QC@O@_?U_GCC@@?', 'NBOI_AG_@B?q_OGC?g?', 'NCA@Q@E[CADGE?@??@G', 'N@Q?_EaOSOa_W?A@?g?',
+    'NQP?oI_?W_CB__AO?`?', 'N?PpPA?cOAW@E??g?D?', 'NSSH@@??[C?hO_CG?a?', 'NKLH?G@_Cc?EOG?`?I?',
+    'NQPC_W_?WGCB_GCA@O?', 'N?osC_a?_oGcOCGA?I?', 'NGQ?_MAOSOa_K?GG@?_', 'NPW?AGCAGMQO_GS??Q?',
+    'N`@b??P?WoPA_AA_?g?', 'NBO?cIGg@@?qO_B??H?', 'NSSJ@@?@[??gCG?a?@_', 'NKE?GPBG_aW?H?A@?B?',
+    'N?Sp@AAc?BW@P?A_?I?', 'NRG??ACAgMQOQ?OO?g?', 'NCOXF?OOC@cAA_@@?S?', 'N@Q?_M_OCOb_W??g?I?',
+    'N?BGS_IGI_SAOOK??P?', 'N?TpOAAcOBO?O@GO?@_', 'N?B?U_IGICSAK?CA@_?', 'NCE@Q@CWCICGCCA@?S?',
+    'NKL@?H@_Cc?EB??`?I?', 'NHQ?_E_OSOa_A@@O?S?', 'NAGu?O@_GMOCO@K?@A?', 'N[CC?CDKIOG_A_@O?@_',
+    'NBOIcAGg@@?a@O?`?H?', 'N`?bOGP?[_P?P?AA?A_', 'NGQ?_MaOCO`_K?C@?I?', 'NBOAcIGg@@?aB??`?H?',
+    'NQOCoI_?WgCAP?AO?@_', 'N@B?U_IGGcS?OAB??A_', 'NO@?oY_?WgCB__S?H??', 'NBOIcIGg@@?o?O?A_A_',
+    'NKDH?@@_SC?UI?CA?g?', 'N@Q?_MAOSOa_W?GG@?_', 'N@OIcA?g@B?qS?AG?g?', 'NHQ?_MAOSOB?GG@@?B?',
+    'N@BGE?IGICSACOCA@O?', 'NA]ACCCGk_?@G@@O?C_', 'NHQ?_M_OSOa_A@?_?CG', 'NRG?AI?AgMQOQ?@??CG',
+    'N@BGU?GGIcSACO?_?CG', 'NCLH?H@_SC?QW?CA?C_', 'NKA_GPBG_aH?_@E??B?', 'NAOIcI?g@A?qK?AG?D?',
+    'NCH?QE@O@o?U`?H?AA?', 'NHQ?_KaOCOa__GA@?I?', 'NGLH?H?_Sc?Uc??O?CG', 'N@@bO?P?[_PAo?AA?g?',
+    'NCE@Q@EW?I@G_AG@AA?', 'NKDH?H@_CC?UI?CA?I?', 'NHQ?_M_OCOB_?g?S?B?', 'N@Gu?O@aGKW?S??Q?C_',
+    'NRW??ICAgIOOOOC@?P?', 'N`@@OGP?[oOAO_H?@?_', 'NCA@Q@A[CGDGE?@G?H?', 'NBW??ICAGMQOg?OO?Q?',
+    'NBGu??@a?IWCAO?a?E?', 'NQPCoI_?W_CAAO@A?@_', 'N?osC_AO`oGCGG@@?I?', 'N@B?S_IGICSAOOCA@_?',
+    'N_@bOGP?[oOAK?A???g', 'N_o_Oh_C_BCO_AC@?a?', 'NKE?GOBG__x?OGH??H?', 'NRO?AICAgKQ?I??`?H?',
+    'NAYACK?Gk_CCE?@G?@_', 'NRW?AICAgKAO_@?O?@G', 'NQ@CoQ_?WgC@Q?@O?A_', 'NQ@CoI_?W_CBQ?AO?`?',
+    'N?DoPAAcOBW?Q?G_?@_', 'NQ@?oW_?WgCB___GH??', 'N@`GSGaO?DoAS?GOA?_', 'N?osC_AOPo?cO@GG?Q?',
+    'NRW?AICA_EOOC@@A?E?', 'NB_GTGaO?DOAP?C@?B?', 'NHA?_IaOSOa_Q?A@?W?', 'NBOIcI?g@@?oAG?Q?A_',
+    'NRW??GCAGMQO_GOO?Q?', 'N@A?U_IGICSAP?CA@_?', 'NAOAcIGg@B?oK?B??A_', 'N?BGU?AGIcSAK?CO@C?',
+    'N`@aOGP?WoP?_AG_?A_', 'NCOXU?QOC@c?GO@@?A_', 'N?ooC_a?pOGc__OCA@?', 'NCJ_QE@C?o?QOCGA?C_',
+    'NQ@COY_?W_CBQ?C_?`?', 'NBGs?O@aGEW?O_@A?C_', 'NBG?AICAgMOOg?Q?A?_', 'NCHH?H@_Sc?QW?E??C_',
+    'N?oSC_aO`oG_H??S?C_', 'N`@aOGO?WoPA_AG_?K?', 'N@@bOGP?Ko@Ao?_@?I?', 'NQPCOW_?W_CB_GC_?`?',
+    'NB?u?O@a?MGC_@I??E?', 'NPW?AICA_MQ?S??`?E?', 'NQ@CoI_?WgC@Q?AO?A_', 'NBW?AACAgIQOg?@O?P?',
+    'N?_cC_AOpoGcQ?GGA_?', 'NCA@Q@C[CI@GG@E??S?', 'NCOPV?OOC@c_B??g?A_', 'NHQ?_MA?SOb?OCGG?__',
+    'NCOXV?OOC@c_?g?C??g', 'N@@bOGO?[_PAo?AA?K?', 'NRO?AICAgAQOI?@A?P?', 'N`@`OGP?[o@?_@O_?A_',
+    'NCH_OE@S@_?U`?OO@@?', 'NQ@C_Y_?Wg?BQ?G@@O?', 'NBOIcAGG@A?q_C@O?D?', 'NPW?AIC?GMQOS?AC?Q?',
+    'NB_?TG_O?DqAP?B??S?', 'NAMACCCGK_CDQ?@O?Q?', 'NQW?AIC?GMQOK?AC?Q?', 'NCOXU?AOC@cAGOCG?__',
+    'NKDH?H@_Sc?SI??C??g', 'N?PpOAAcOBO@O@GOB??', 'NBGU?O@aGIW?H??a?C_', 'NQ@CoY_?W?CBQ?CA?`?',
+    'NHQ?_M_OSOB?@@?g?B?', 'N?SpPAAcOBW?P??A??g', 'NGQ?_MaOCOb?K?@@?I?', 'NCOXU?QOC@c_GO?C??g',
+    'NQW?AG?AgMQO_GK??c?', 'N@AGU?IGICSAP?COA@?', 'NKHH?G@_Sc?EOGE??O_', 'N?_sC_aO`OGcQ?CA?I?',
+    'N?]ACK?Gk_CDO?C?_c?', 'N?_sC_aOooGCQ?GA?__', 'N?_SC_aOpoG_Q?H??C_', 'NA]ACGCGk?C@CA?o?C_',
+    'NQPC_I_?WgCAA_AO?@_', 'NKDH?H?_Sc?UG?A?_K?', 'NC?XV?QOC@?aQ?G@?B?', 'NSSG@?O@[C?hO_OGCO?',
+    'NRO?AACAgMQOI?@??GG', 'NGE_?PBG_Ax?c?CA?o?', 'N?ocC_AOp_GcGGD?@@?', 'NRW?AI?AgMAO_@@??CG',
+    'NAGu??@aGMW?K?AO?C_', 'NQP?_Q_?WgCB__A_?g?', 'NCE@Q?EWCID?OGCC?G_', 'N`@b?GP?OoPA_AA_?E?',
+    'NQOC_Q_?WgCBP?A_?g?', 'NSOJ@@O@[??gE??a?@_', 'NgA?HOIe?@E@OOD??P?', 'NSSJ@??@[C?`OGCG?G_',
+    'NCE@Q@AKCGDGOC@G?H?', 'NRW?AGC?gIQO_GAC?P?', 'NQ@CoY_?G_CBQ?@A?I?', 'N?DpOAAcOBW@O?A?cG?',
+    'NHQ?_CAOSOb__GGG?g?', 'NKA_?PBG_ax?C?A?_o?', 'NKL@?G@_Cc?UOGB??I?', 'NPW?AIC?_MQOS?AC?E?',
+    'NHQ?_CaOSOb__??G_g?', 'NRW?AG?AgMOO_GC@?c?', 'N?osC_aOP_GcAA?_?AG', 'NGQ?_IaOSOb_G?C?_W?',
+    'NKE_G?BG__x?OGAO?H?', 'NCHH?@@_Sc?UW?E??g?', 'N?osC?a?poG_OCCO?C_', 'N?TpPAA_O@W?CC?Q?@_',
+    'N`@bOGO?[O@A_@CA?K?', 'NCJ_QA?S@o?S?o?W?A_', 'NHQ?_KaOCOb__G?O?AG', 'NSSB@??@[C?hOGCG@_?',
+    'NCJ_AE?S@o?SA_?W?A_', 'N?_cC_aOPoGcQ?D??Q?', 'NRO?A?CAgMQO_GI??g?', 'N`?b?GP?[oOAP?A_@?_',
+    'NQ@C_Y_?WGCBQ?CA@O?', 'N?T`@AAc?BW@D?A_?I?', 'N`@bO?P?WoPA_??A_g?', 'N?DpPAAc?BW@O?A?_I?',
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