------------ complete table for m up to 16 and all n ----- Counts for 1 edge: on 2 vertices, 1 is connected, 0 not Altogether 1 connected and 0 not. Counts for 2 edges: on 3 vertices, 2 are connected, 0 not Altogether 2 connected and 0 not. Counts for 3 edges: on 3 vertices, 2 are connected, 0 not on 4 vertices, 4 are connected, 0 not Altogether 6 connected and 0 not. Counts for 4 edges: on 4 vertices, 12 are connected, 0 not on 5 vertices, 12 are connected, 0 not Altogether 24 connected and 0 not. Counts for 5 edges: on 4 vertices, 8 are connected, 0 not on 5 vertices, 68 are connected, 0 not on 6 vertices, 40 are connected, 4 not Altogether 116 connected and 4 not. Counts for 6 edges: on 4 vertices, 2 are connected, 0 not on 5 vertices, 106 are connected, 0 not on 6 vertices, 400 are connected, 6 not on 7 vertices, 164 are connected, 42 not Altogether 672 connected and 48 not. Counts for 7 edges: on 5 vertices, 88 are connected, 0 not on 6 vertices, 1184 are connected, 2 not on 7 vertices, 2496 are connected, 148 not on 8 vertices, 752 are connected, 370 not Altogether 4520 connected and 520 not. Counts for 8 edges: on 5 vertices, 32 are connected, 0 not on 6 vertices, 1728 are connected, 0 not on 7 vertices, 11932 are connected, 164 not on 8 vertices, 17338 are connected, 2118 not on 9 vertices, 4020 are connected, 2988 not Altogether 35050 connected and 5270 not. Counts for 9 edges: on 5 vertices, 8 are connected, 0 not on 6 vertices, 1696 are connected, 0 not on 7 vertices, 29444 are connected, 92 not on 8 vertices, 121084 are connected, 5220 not on 9 vertices, 127660 are connected, 28300 not on 10 vertices, 23576 are connected, 25800 not Altogether 303468 connected and 59412 not. Counts for 10 edges: on 6 vertices, 964 are connected, 0 not on 7 vertices, 45472 are connected, 24 not on 8 vertices, 442222 are connected, 6290 not on 9 vertices, 1259838 are connected, 106154 not on 10 vertices, 1030524 are connected, 349952 not on 11 vertices, 155632 are connected, 231728 not Altogether 2934652 connected and 694148 not. Counts for 11 edges: on 6 vertices, 432 are connected, 0 not on 7 vertices, 50292 are connected, 2 not on 8 vertices, 1051048 are connected, 5338 not on 9 vertices, 6488844 are connected, 231456 not on 10 vertices, 13590300 are connected, 1960288 not on 11 vertices, 8852398 are connected, 4353120 not on 12 vertices, 1112032 are connected, 2221250 not Altogether 31145346 connected and 8771454 not. Counts for 12 edges: on 6 vertices, 104 are connected, 0 not on 7 vertices, 40176 are connected, 0 not on 8 vertices, 1744982 are connected, 2458 not on 9 vertices, 21410862 are connected, 325418 not on 10 vertices, 93887854 are connected, 6283146 not on 11 vertices, 153385084 are connected, 33476756 not on 12 vertices, 82121018 are connected, 54918198 not on 13 vertices, 8733628 are connected, 22671916 not Altogether 361323708 connected and 117677892 not. Counts for 13 edges: on 6 vertices, 24 are connected, 0 not on 7 vertices, 24688 are connected, 0 not on 8 vertices, 2250864 are connected, 1012 not on 9 vertices, 51470648 are connected, 334460 not on 10 vertices, 420080516 are connected, 13837108 not on 11 vertices, 1378054500 are connected, 151780972 not on 12 vertices, 1803091192 are connected, 562807828 not on 13 vertices, 806839236 are connected, 716685608 not on 14 vertices, 73547332 are connected, 246214812 not Altogether 4535359000 connected and 1691661800 not. Counts for 14 edges: on 7 vertices, 11208 are connected, 0 not on 8 vertices, 2184056 are connected, 120 not on 9 vertices, 92513144 are connected, 242272 not on 10 vertices, 1340857860 are connected, 21548304 not on 11 vertices, 7975757616 are connected, 460753376 not on 12 vertices, 20604457050 are connected, 3361526958 not on 13 vertices, 22263918324 are connected, 9379492500 not on 14 vertices, 8481362264 are connected, 9678527484 not on 15 vertices, 670789524 are connected, 2844349140 not Altogether 61431851046 connected and 25746440154 not. Counts for 15 edges: on 7 vertices, 3780 are connected, 0 not on 8 vertices, 1818244 are connected, 0 not on 9 vertices, 136668880 are connected, 133504 not on 10 vertices, 3335302886 are connected, 26953778 not on 11 vertices, 33380409234 are connected, 1059739642 not on 12 vertices, 151167588580 are connected, 13895261452 not on 13 vertices, 315541333316 are connected, 72653526068 not on 14 vertices, 286284099998 are connected, 158792607722 not on 15 vertices, 93933923996 are connected, 136148684460 not on 16 vertices, 6502948232 are connected, 34813364228 not Altogether 890284097146 connected and 417390270854 not. Counts for 16 edges: on 7 vertices, 864 are connected, 0 not on 8 vertices, 1141312 are connected, 0 not on 9 vertices, 159551124 are connected, 50812 not on 10 vertices, 6537511962 are connected, 25011238 not on 11 vertices, 106698003000 are connected, 1838165696 not on 12 vertices, 795992914532 are connected, 42044961052 not on 13 vertices, 2869123162654 are connected, 382921672314 not on 14 vertices, 4974721374674 are connected, 1533425714350 not on 15 vertices, 3859250594040 are connected, 2731211403920 not on 16 vertices, 1104325114202 are connected, 1995326513702 not on 17 vertices, 67540932632 are connected, 451646093920 not Altogether 13784350300996 connected and 7138439587004 not. ------------- complete table for n up to 10 and all m>16 ----- Counts for 17 edges and at most 10 vertices: on 7 vertices, 168 are connected, 0 not on 8 vertices, 621316 are connected, 0 not on 9 vertices, 160223172 are connected, 16120 not on 10 vertices, 10768945832 are connected, 19561088 not Altogether 10929790488 connected and 19577208 not. Counts for 18 edges and at most 10 vertices: on 8 vertices, 261424 are connected, 0 not on 9 vertices, 132942576 are connected, 1584 not on 10 vertices, 14731273632 are connected, 11659252 not Altogether 14864477632 connected and 11660836 not. Counts for 19 edges and at most 10 vertices: on 8 vertices, 98880 are connected, 0 not on 9 vertices, 96718744 are connected, 384 not on 10 vertices, 17608019380 are connected, 6130148 not Altogether 17704837004 connected and 6130532 not. Counts for 20 edges and at most 10 vertices: on 8 vertices, 24264 are connected, 0 not on 9 vertices, 57595128 are connected, 16 not on 10 vertices, 17714464748 are connected, 2229380 not Altogether 17772084140 connected and 2229396 not. Counts for 21 edges and at most 10 vertices: on 8 vertices, 6032 are connected, 0 not on 9 vertices, 31256672 are connected, 0 not on 10 vertices, 16191345776 are connected, 752688 not Altogether 16222608480 connected and 752688 not. Counts for 22 edges and at most 10 vertices: on 8 vertices, 904 are connected, 0 not on 9 vertices, 13767240 are connected, 0 not on 10 vertices, 12533585044 are connected, 165596 not Altogether 12547353188 connected and 165596 not. Counts for 23 edges and at most 10 vertices: on 8 vertices, 128 are connected, 0 not on 9 vertices, 5620288 are connected, 0 not on 10 vertices, 8904987452 are connected, 36732 not Altogether 8910607868 connected and 36732 not. Counts for 24 edges and at most 10 vertices: on 9 vertices, 1749044 are connected, 0 not on 10 vertices, 5394129604 are connected, 2000 not Altogether 5395878648 connected and 2000 not. Counts for 25 edges and at most 10 vertices: on 9 vertices, 476928 are connected, 0 not on 10 vertices, 3018393464 are connected, 96 not Altogether 3018870392 connected and 96 not. Counts for 26 edges and at most 10 vertices: on 9 vertices, 97808 are connected, 0 not on 10 vertices, 1433363840 are connected, 0 not Altogether 1433461648 connected and 0 not. Counts for 27 edges and at most 10 vertices: on 9 vertices, 18608 are connected, 0 not on 10 vertices, 629038400 are connected, 0 not Altogether 629057008 connected and 0 not. Counts for 28 edges and at most 10 vertices: on 9 vertices, 1920 are connected, 0 not on 10 vertices, 234506400 are connected, 0 not Altogether 234508320 connected and 0 not. Counts for 29 edges and at most 10 vertices: on 9 vertices, 640 are connected, 0 not on 10 vertices, 82524632 are connected, 0 not Altogether 82525272 connected and 0 not. Counts for 30 edges and at most 10 vertices: on 10 vertices, 22230800 are connected, 0 not Altogether 22230800 connected and 0 not. Counts for 31 edges and at most 10 vertices: on 10 vertices, 5500552 are connected, 0 not Altogether 5500552 connected and 0 not. Counts for 32 edges and at most 10 vertices: on 10 vertices, 1021888 are connected, 0 not Altogether 1021888 connected and 0 not. Counts for 33 edges and at most 10 vertices: on 10 vertices, 209936 are connected, 0 not Altogether 209936 connected and 0 not. Counts for 34 edges and at most 10 vertices: on 10 vertices, 15504 are connected, 0 not Altogether 15504 connected and 0 not. Counts for 35 edges and at most 10 vertices: on 10 vertices, 5376 are connected, 0 not Altogether 5376 connected and 0 not. Counts for 36 edges and at most 10 vertices: on 10 vertices, 768 are connected, 0 not Altogether 768 connected and 0 not.