2516:
870:
2450:
2304:
2384:
2288:
74:
2582:
2318:
2683:
312:
2272:
707:
2697:
2669:
2334:
750:
606:
1060:
200:
214:
2094:
1440:
1403:
1366:
1218:
1181:
820:
1983:
1329:
1292:
1255:
1653:
792:
806:
778:
2057:
2020:
256:
2768:
1046:
340:
270:
1743:
1700:
1610:
2754:
410:
480:
764:
326:
116:
158:
2782:
996:
735:
721:
2711:
940:
693:
466:
550:
1032:
2852:
564:
186:
508:
494:
130:
88:
298:
144:
522:
2655:
898:
2838:
679:
438:
242:
2162:
856:
665:
2796:
2866:
1074:
926:
651:
452:
354:
172:
102:
2824:
592:
396:
2810:
982:
884:
382:
228:
284:
968:
912:
578:
536:
424:
1010:
954:
368:
2981:
2919:
3196:
3056:
2344:
An algorithm to generate all the non-isomorphic fullerenes with a given number of hexagonal faces has been developed by G. Brinkmann and A. Dress. G. Brinkmann also provided a freely available implementation, called
2515:
2449:
2581:
2383:
1778:
1735:
1688:
1645:
1574:
1515:
3036:
3009:
2123:
2086:
2049:
2012:
1974:
1944:
1914:
1884:
1842:
1601:
1469:
1432:
1395:
1358:
1321:
1284:
1247:
1210:
1168:
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2614:
2574:
2548:
2508:
2442:
2482:
2416:
1541:
1811:
1139:
1118:
3047:
This partial list contains definitions of graphs and graph families which are known by particular names, but do not have a
Knowledge article of their own.
1652:
2287:
3513:
3527:
2093:
2317:
1982:
1439:
1402:
1365:
1328:
1291:
1254:
1217:
1180:
2056:
2019:
1742:
1699:
1609:
3410:
3482:
3327:
2271:
415:
3321:
3623:
869:
58:
have names, sometimes inspired by the graph's topology, and sometimes after their discoverer. A famous example is the
2294:
3117:
2303:
706:
62:, a concrete graph on 10 vertices that appears as a minimal example or counterexample in many different contexts.
3083:, is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a
2682:
2696:
213:
199:
73:
219:
205:
17:
2237:
indicate the number of vertices, edges, and faces), that there are exactly 12 pentagons in a fullerene and
849:
lists all small symmetric 3-regular graphs. Every strongly regular graph is symmetric, but not vice versa.
30:
311:
1691:
712:
555:
791:
749:
2668:
2767:
1059:
875:
777:
2333:
783:
2753:
269:
2896:
2829:
2710:
1481:
734:
275:
47:
3633:
3149:, is a graph obtained by attaching a single edge and node to each node of the outer circuit of a
2815:
945:
819:
605:
549:
325:
2823:
2702:
939:
805:
797:
629:
597:
409:
339:
331:
2809:
2781:
2654:
995:
720:
521:
255:
2716:
2660:
2324:
1750:
1707:
1660:
1617:
1546:
1487:
1001:
763:
726:
479:
115:
1045:
692:
465:
3365:
3014:
2987:
2729:
2688:
2210:
2101:
2064:
2027:
1990:
1952:
1922:
1892:
1862:
1820:
1579:
1447:
1410:
1373:
1336:
1299:
1262:
1225:
1188:
1146:
698:
157:
3344:
Brinkmann, Gunnar; Dress, Andreas W.M (1997). "A Constructive
Enumeration of Fullerenes".
2619:
2593:
2553:
2527:
2487:
2421:
591:
507:
493:
143:
87:
8:
3578:
3178:
3174:
2884:
2461:
2395:
1520:
1031:
897:
527:
297:
2851:
2837:
678:
563:
437:
241:
3437:
3419:
2309:
1796:
1124:
1103:
842:
185:
2865:
1073:
925:
855:
664:
650:
451:
395:
353:
171:
129:
101:
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3565:
3548:
3507:
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3380:
2795:
2787:
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1009:
981:
883:
769:
381:
303:
227:
3429:
3353:
3274:
3182:
2733:
2262:
2135:
755:
471:
283:
967:
911:
577:
535:
423:
163:
3628:
3361:
3331:
2389:
2370:
1065:
903:
838:
513:
499:
149:
121:
93:
79:
51:
953:
367:
34:
contains definitions of graphs and graph families. For collected definitions of
3489:
3458:
3405:
3383:
3325:
2843:
2744:
2674:
2358:
1097:
684:
611:
443:
345:
247:
59:
3597:
845:) taking any ordered pair of adjacent vertices to any other ordered pair; the
191:
3617:
2871:
2740:
2209:
with all faces of size 5 or 6 (including the external face). It follows from
2202:
1079:
1037:
931:
861:
846:
825:
670:
656:
485:
457:
401:
359:
317:
177:
107:
3357:
2857:
2801:
2521:
2278:
2206:
987:
973:
889:
811:
569:
387:
289:
261:
233:
55:
35:
3408:(2010), "Combinatorics and geometry of finite and infinite squaregraphs",
2973:
vertices constructed by connecting a single vertex to every vertex in an (
3236:
3150:
3113:
3084:
2960:
2736:
2587:
2362:
2149:
1790:
917:
740:
583:
541:
429:
3551:
2455:
1051:
1016:
959:
373:
135:
50:. For links to existing articles about particular kinds of graphs, see
3433:
3602:
3556:
3463:
3388:
2346:
2197:
2161:
2374:
3424:
3177:
in which all the vertices are within distance 2 of a central
2366:
2980:
2918:
3195:
3055:
3207:
2365:, and more generally the complete graphs form skeletons of
38:
terms that do not refer to individual graph types, such as
3247:, with corresponding vertices connected by "spokes". Thus
3546:
3403:
3320:
Gallian, J. A. "Dynamic Survey DS6: Graph
Labeling."
3017:
2990:
2622:
2596:
2556:
2530:
2490:
2464:
2424:
2398:
2104:
2067:
2030:
1993:
1955:
1925:
1895:
1865:
1823:
1799:
1753:
1710:
1663:
1620:
1582:
1549:
1523:
1490:
1450:
1413:
1376:
1339:
1302:
1265:
1228:
1191:
1149:
1127:
1106:
3477:
3475:
3453:
3378:
3280:A web graph has also been defined as a prism graph
3592:
3030:
3003:
2634:
2608:
2568:
2542:
2502:
2476:
2436:
2410:
2117:
2080:
2043:
2006:
1968:
1938:
1908:
1878:
1836:
1805:
1772:
1729:
1682:
1639:
1595:
1568:
1535:
1509:
1463:
1426:
1389:
1352:
1315:
1278:
1241:
1204:
1162:
1133:
1112:
2373:are also skeletons of higher-dimensional regular
3615:
3472:
3120:of squaregraphs. Gear graphs are also known as
3343:
54:. Some of the finite structures considered in
3292:, with the edges of the outer cycle removed.
1475:
2361:on four vertices forms the skeleton of the
2265:of the corresponding fullerene compounds.
1543:see the section on star graphs. The graph
623:
618:
3423:
3194:
3054:
2979:
2917:
2739:that requires four colors in any proper
2160:
1023:
14:
3616:
3512:: CS1 maint: archived copy as title (
2245:/2 – 10 hexagons. Therefore
3593:
3547:
3454:
3379:
1916:, and then several with Greek naming
841:is one in which there is a symmetry (
3411:SIAM Journal on Discrete Mathematics
2129:
65:
3322:Electronic Journal of Combinatorics
3309:A Logical Approach to Discrete Math
3307:David Gries and Fred B. Schneider,
3112:edges. Gear graphs are examples of
2646:
2190:
832:
24:
2352:
1091:
25:
3645:
2295:Hexagonal truncated trapezohedron
1086:
3118:forbidden graph characterization
2864:
2850:
2836:
2822:
2808:
2794:
2780:
2766:
2752:
2709:
2695:
2681:
2667:
2653:
2580:
2514:
2448:
2382:
2332:
2316:
2302:
2286:
2270:
2092:
2055:
2018:
1981:
1741:
1698:
1651:
1608:
1603:(the square) introduced below.
1438:
1401:
1364:
1327:
1290:
1253:
1216:
1179:
1072:
1058:
1044:
1030:
1008:
994:
980:
966:
952:
938:
924:
910:
896:
882:
868:
854:
818:
804:
790:
776:
762:
748:
733:
719:
705:
691:
677:
663:
649:
604:
590:
576:
562:
548:
534:
520:
506:
492:
478:
464:
450:
436:
422:
408:
394:
380:
366:
352:
338:
324:
310:
296:
282:
268:
254:
240:
226:
212:
198:
184:
170:
156:
142:
128:
114:
100:
86:
72:
3586:
3042:
2954:
3540:
3520:
3447:
3397:
3372:
3337:
3324:, DS6, 1-58, January 3, 2007.
3314:
3301:
2144:can be constructed by joining
13:
1:
3295:
3116:, and play a key role in the
2977: − 1)-cycle.
2257: = 30 + 3
2249: = 20 + 2
1120:vertices is often called the
3404:Bandelt, H.-J.; Chepoi, V.;
2743:. The smallest snark is the
7:
2261:. Fullerene graphs are the
10:
3650:
3552:Graph.html "Lobster Graph"
3164:
2915:is called the claw graph.
2211:Euler's polyhedron formula
2195:In graph theory, the term
3624:Mathematics-related lists
3528:"Google Discussiegroepen"
3235:concentric copies of the
3231:is a graph consisting of
2723:
1856:. Special cases are the
1784:
1476:Complete bipartite graphs
220:Ellingham–Horton 78-graph
206:Ellingham–Horton 54-graph
3311:, Springer, 1993, p 436.
2897:complete bipartite graph
2830:Loupekine snark (second)
2747:, already listed above.
2263:Schlegel representations
1482:complete bipartite graph
48:Glossary of graph theory
3131:
3050:
2878:
2816:Loupekine snark (first)
1813:vertices is called the
1773:{\displaystyle K_{3,4}}
1730:{\displaystyle K_{2,4}}
1683:{\displaystyle K_{3,3}}
1640:{\displaystyle K_{2,3}}
1569:{\displaystyle K_{2,2}}
1510:{\displaystyle K_{n,m}}
713:Hoffman–Singleton graph
640:is usually denoted srg(
624:Strongly regular graphs
619:Highly symmetric graphs
3358:10.1006/jagm.1996.0806
3211:
3190:
3067:
3039:
3032:
3005:
2951:
2774:Blanuša snark (second)
2703:Truncated dodecahedron
2636:
2610:
2570:
2544:
2504:
2478:
2438:
2412:
2225: = 2 (where
2187:
2165:The friendship graphs
2158:with a common vertex.
2119:
2082:
2045:
2008:
1970:
1940:
1910:
1880:
1844:. It is also called a
1838:
1807:
1774:
1731:
1684:
1641:
1597:
1570:
1537:
1511:
1465:
1428:
1391:
1354:
1317:
1280:
1243:
1206:
1164:
1135:
1114:
798:Local McLaughlin graph
630:strongly regular graph
3346:Journal of Algorithms
3257:is the same graph as
3198:
3058:
3033:
3031:{\displaystyle W_{9}}
3006:
3004:{\displaystyle W_{4}}
2983:
2921:
2760:Blanuša snark (first)
2717:Truncated icosahedron
2661:Truncated tetrahedron
2637:
2611:
2571:
2545:
2505:
2479:
2439:
2413:
2325:truncated icosahedral
2164:
2120:
2118:{\displaystyle C_{6}}
2083:
2081:{\displaystyle C_{5}}
2046:
2044:{\displaystyle C_{4}}
2009:
2007:{\displaystyle C_{3}}
1971:
1969:{\displaystyle C_{6}}
1941:
1939:{\displaystyle C_{5}}
1911:
1909:{\displaystyle C_{4}}
1881:
1879:{\displaystyle C_{3}}
1839:
1837:{\displaystyle C_{n}}
1808:
1775:
1732:
1685:
1642:
1598:
1596:{\displaystyle C_{4}}
1571:
1538:
1512:
1466:
1464:{\displaystyle K_{8}}
1429:
1427:{\displaystyle K_{7}}
1392:
1390:{\displaystyle K_{6}}
1355:
1353:{\displaystyle K_{5}}
1318:
1316:{\displaystyle K_{4}}
1281:
1279:{\displaystyle K_{3}}
1244:
1242:{\displaystyle K_{2}}
1207:
1205:{\displaystyle K_{1}}
1165:
1163:{\displaystyle K_{n}}
1136:
1115:
1024:Semi-symmetric graphs
784:Brouwer–Haemers graph
556:Young–Fibonacci graph
3015:
2988:
2689:Truncated octahedron
2635:{\displaystyle m=30}
2620:
2609:{\displaystyle n=12}
2594:
2569:{\displaystyle m=30}
2554:
2543:{\displaystyle n=20}
2528:
2503:{\displaystyle m=12}
2488:
2462:
2437:{\displaystyle m=12}
2422:
2396:
2102:
2065:
2028:
1991:
1953:
1923:
1893:
1863:
1821:
1817:and usually denoted
1797:
1751:
1708:
1661:
1618:
1580:
1547:
1521:
1488:
1448:
1411:
1374:
1337:
1300:
1263:
1226:
1189:
1147:
1143:and usually denoted
1125:
1104:
276:Goldner–Harary graph
2477:{\displaystyle n=6}
2411:{\displaystyle n=8}
1576:equals the 4-cycle
1536:{\displaystyle n=1}
1484:is usually denoted
946:Tutte–Coxeter graph
876:Möbius–Kantor graph
3595:Weisstein, Eric W.
3549:Weisstein, Eric W.
3456:Weisstein, Eric W.
3381:Weisstein, Eric W.
3330:2012-01-31 at the
3212:
3068:
3040:
3028:
3001:
2952:
2632:
2606:
2566:
2540:
2500:
2474:
2434:
2408:
2310:26-fullerene graph
2188:
2115:
2078:
2041:
2004:
1966:
1936:
1906:
1876:
1834:
1803:
1770:
1727:
1680:
1637:
1593:
1566:
1533:
1507:
1461:
1424:
1387:
1350:
1313:
1276:
1239:
1202:
1160:
1131:
1110:
843:graph automorphism
636:vertices and rank
598:Wiener–Araya graph
332:Harries–Wong graph
3434:10.1137/090760301
3108:+1 vertices and 3
2788:Double-star snark
2130:Friendship graphs
1806:{\displaystyle n}
1134:{\displaystyle n}
1113:{\displaystyle n}
1002:Biggs–Smith graph
727:Higman–Sims graph
66:Individual graphs
16:(Redirected from
3641:
3609:
3608:
3607:
3590:
3584:
3583:
3582:
3576:
3571:
3569:
3561:
3544:
3538:
3537:
3535:
3534:
3524:
3518:
3517:
3511:
3503:
3501:
3500:
3494:
3488:. Archived from
3487:
3479:
3470:
3469:
3468:
3451:
3445:
3444:
3427:
3418:(4): 1399–1440,
3401:
3395:
3394:
3393:
3376:
3370:
3369:
3341:
3335:
3318:
3312:
3305:
3126:bipartite wheels
3037:
3035:
3034:
3029:
3027:
3026:
3010:
3008:
3007:
3002:
3000:
2999:
2922:The star graphs
2868:
2854:
2840:
2826:
2812:
2798:
2784:
2770:
2756:
2713:
2699:
2685:
2671:
2657:
2647:Truncated solids
2641:
2639:
2638:
2633:
2615:
2613:
2612:
2607:
2584:
2575:
2573:
2572:
2567:
2549:
2547:
2546:
2541:
2518:
2509:
2507:
2506:
2501:
2483:
2481:
2480:
2475:
2452:
2443:
2441:
2440:
2435:
2417:
2415:
2414:
2409:
2386:
2371:hypercube graphs
2336:
2320:
2306:
2290:
2274:
2201:refers to any 3-
2191:Fullerene graphs
2136:friendship graph
2124:
2122:
2121:
2116:
2114:
2113:
2096:
2087:
2085:
2084:
2079:
2077:
2076:
2059:
2050:
2048:
2047:
2042:
2040:
2039:
2022:
2013:
2011:
2010:
2005:
2003:
2002:
1985:
1975:
1973:
1972:
1967:
1965:
1964:
1945:
1943:
1942:
1937:
1935:
1934:
1915:
1913:
1912:
1907:
1905:
1904:
1885:
1883:
1882:
1877:
1875:
1874:
1843:
1841:
1840:
1835:
1833:
1832:
1812:
1810:
1809:
1804:
1779:
1777:
1776:
1771:
1769:
1768:
1745:
1736:
1734:
1733:
1728:
1726:
1725:
1702:
1689:
1687:
1686:
1681:
1679:
1678:
1655:
1646:
1644:
1643:
1638:
1636:
1635:
1612:
1602:
1600:
1599:
1594:
1592:
1591:
1575:
1573:
1572:
1567:
1565:
1564:
1542:
1540:
1539:
1534:
1516:
1514:
1513:
1508:
1506:
1505:
1470:
1468:
1467:
1462:
1460:
1459:
1442:
1433:
1431:
1430:
1425:
1423:
1422:
1405:
1396:
1394:
1393:
1388:
1386:
1385:
1368:
1359:
1357:
1356:
1351:
1349:
1348:
1331:
1322:
1320:
1319:
1314:
1312:
1311:
1294:
1285:
1283:
1282:
1277:
1275:
1274:
1257:
1248:
1246:
1245:
1240:
1238:
1237:
1220:
1211:
1209:
1208:
1203:
1201:
1200:
1183:
1169:
1167:
1166:
1161:
1159:
1158:
1140:
1138:
1137:
1132:
1119:
1117:
1116:
1111:
1076:
1062:
1048:
1034:
1012:
998:
984:
970:
956:
942:
928:
914:
900:
886:
872:
858:
833:Symmetric graphs
822:
808:
794:
780:
766:
756:Shrikhande graph
752:
737:
723:
709:
699:Hall–Janko graph
695:
681:
667:
653:
608:
594:
580:
566:
552:
538:
528:Tutte's fragment
524:
510:
496:
482:
472:Sousselier graph
468:
454:
440:
426:
412:
398:
384:
370:
356:
342:
328:
314:
300:
286:
272:
258:
244:
230:
216:
202:
188:
174:
160:
146:
132:
118:
104:
90:
76:
21:
3649:
3648:
3644:
3643:
3642:
3640:
3639:
3638:
3614:
3613:
3612:
3591:
3587:
3574:
3572:
3563:
3562:
3545:
3541:
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52:Category:Graphs
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1157:
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60:Petersen graph
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3495:on 2012-01-31
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1692:utility graph
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1080:Tutte 12-cage
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1038:Folkman graph
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932:Coxeter graph
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919:
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891:
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871:
866:
863:
862:Heawood graph
857:
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827:
826:Gewirtz graph
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27:This partial
19:
18:Lobster graph
3601:
3588:
3555:
3542:
3531:. Retrieved
3522:
3497:. Retrieved
3490:the original
3462:
3459:"Helm graph"
3449:
3415:
3409:
3406:Eppstein, D.
3399:
3387:
3384:"Gear graph"
3374:
3349:
3345:
3339:
3316:
3308:
3303:
3286:
3282:
3281:
3279:
3267:
3262:
3258:
3252:
3248:
3243:
3239:
3232:
3227:
3223:
3219:
3215:
3213:
3200:
3183:
3170:
3168:
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3153:
3142:
3141:
3137:
3135:
3125:
3121:
3114:squaregraphs
3109:
3105:
3100:
3096:
3091:
3087:
3079:
3075:
3071:
3069:
3063:
3059:
3046:
3043:Other graphs
2974:
2970:
2963:
2958:
2955:Wheel graphs
2944:
2937:
2930:
2923:
2909:
2904:
2899:
2891:
2887:
2882:
2858:Tietze graph
2802:Flower snark
2727:
2522:Dodecahedron
2356:
2343:
2339:70-fullerene
2279:dodecahedral
2258:
2254:
2250:
2246:
2242:
2238:
2234:
2230:
2226:
2222:
2218:
2214:
2207:planar graph
2196:
2194:
2180:
2173:
2166:
2152:
2145:
2138:
2133:
1947:
1917:
1887:
1857:
1853:
1849:
1846:cyclic graph
1845:
1814:
1788:
1479:
1171:
1121:
1095:
988:Foster graph
890:Pappus graph
836:
812:Perkel graph
641:
637:
633:
627:
570:Wagner graph
388:Horton graph
290:Golomb graph
262:Frucht graph
234:Errera graph
56:graph theory
43:
39:
36:graph theory
28:
26:
3598:"Web graph"
3237:cycle graph
3184:caterpillar
3181:. Compare
3173:graph is a
3151:wheel graph
3085:wheel graph
2961:wheel graph
2908:. The star
2737:cubic graph
2588:Icosahedron
2363:tetrahedron
2150:cycle graph
1791:cycle graph
974:Klein graph
918:Nauru graph
743:of order 13
741:Paley graph
584:Wells graph
542:Tutte graph
430:McGee graph
192:DĂĽrer graph
3618:Categories
3575:|url=
3533:2014-02-05
3499:2008-08-16
3296:References
3140:, denoted
3138:helm graph
3074:, denoted
3072:gear graph
2734:bridgeless
2456:Octahedron
1052:Gray graph
1017:Rado graph
960:Dyck graph
374:Holt graph
136:Bull graph
3603:MathWorld
3557:MathWorld
3464:MathWorld
3425:0905.4537
3389:MathWorld
3122:cogwheels
2375:polytopes
2367:simplices
2198:fullerene
3566:cite web
3508:cite web
3442:10788524
3328:Archived
3095:. Thus,
1918:pentagon
1858:triangle
1172:komplett
29:list of
3577:value (
3366:1441972
3171:lobster
3165:Lobster
2984:Wheels
2895:is the
2347:fullgen
2203:regular
1976:, etc.
1948:hexagon
1852:or the
1850:polygon
1815:n-cycle
1141:-clique
644:,λ,μ).
3629:Graphs
3573:Check
3440:
3364:
3266:, and
3218:graph
2724:Snarks
2369:. The
2327:graph)
2297:graph)
2281:graph)
1888:square
1886:, the
1785:Cycles
1690:, the
1517:. For
46:, see
40:vertex
31:graphs
3493:(PDF)
3486:(PDF)
3438:S2CID
3420:arXiv
3289:+1, 3
3275:prism
3273:is a
3206:is a
3104:has 2
2732:is a
2730:snark
1854:n-gon
3579:help
3514:link
3214:The
3208:cube
3179:path
3175:tree
3132:Helm
3124:and
3051:Gear
2959:The
2943:and
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2879:Star
2390:Cube
2357:The
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1789:The
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