727:
614:
Faber, V.; Moore, J.W. (1988), "High-degree low-diameter interconnection networks with vertex symmetry:the directed case",
558:
Cayley digraphs found by
Michael J. Dinneen. The complete set of cayley digraphs in that order was found by Eyal Loz.
534:
Digraph found by V.Faber and J.W.Moore. The complete set of cayley digraphs in that order was found by Eyal Loz.
755:
574:
Cayley digraph found by Paul Hafner. The complete set of cayley digraphs in that order was found by Eyal Loz.
550:
Cayley digraphs found by
Michael J. Dinneen. Details about this graph are available in a paper by the author.
24:
17:
542:
Digraphs found by
Francesc Comellas and M. A. Fiol. More details are available in a paper by the authors.
31:
Table of the orders of the largest known vertex-symmetric graphs for the directed degree diameter problem
566:
Cayley digraphs found by Paul Hafner. Details about this graph are available in a paper by the author.
590:
Cayley digraphs found by Eyal Loz. More details are available in a paper by Eyal Loz and Jozef Širáň.
526:
Family of digraphs found by V.Faber and J.W.Moore. More details are available also by other authors.
633:
665:
643:
624:
J. Dinneen, Michael; Hafner, Paul R. (1994), "New
Results for the Degree/Diameter Problem",
518:
Family of digraphs found by W.H.Kautz. More details are available in a paper by the author.
733:
20:
603:
Kautz, W.H. (1969), "Design of optimal interconnection networks for multiprocessors",
749:
739:
702:
670:
680:
656:
Comellas, F.; Fiol, M.A. (1995), "Vertex-symmetric digraphs with small diameter",
684:
605:
Architecture and Design of
Digital Computers, Nato Advanced Summer Institute
647:
638:
685:"Moore graphs and beyond: A survey of the degree/diameter problem"
616:
Technical Report LA-UR-88-1051, los Alamos
National Laboratory
734:
The Degree - Diameter
Problem on CombinatoricsWiki.org
703:"New record graphs in the degree-diameter problem"
8:
669:
637:
503:
34:
710:Australasian Journal of Combinatorics
23:(as of October 2008) in the directed
7:
692:Electronic Journal of Combinatorics
14:
701:Loz, Eyal; Širáň, Jozef (2008),
1:
742:Degree-Diameter problem page.
671:10.1016/0166-218X(93)E0145-O
658:Discrete Applied Mathematics
582:Digraphs found by J. Gómez.
772:
728:Vertex-symmetric Digraphs
683:; Širáň, Jozef (2005),
25:Degree diameter problem
648:10.1002/net.3230240702
27:are tabulated below.
694:, Dynamic, survey D
594:
593:
497:
496:
18:vertex transitive
763:
717:
707:
695:
689:
674:
673:
650:
641:
618:
608:
504:
493:115 430 515 200
35:
771:
770:
766:
765:
764:
762:
761:
760:
756:Directed graphs
746:
745:
724:
705:
700:
687:
679:
655:
623:
613:
602:
599:
502:
458:47 703 427 200
423:18 065 203 200
43:
40:
33:
16:The best known
12:
11:
5:
769:
767:
759:
758:
748:
747:
744:
743:
737:
731:
723:
722:External links
720:
719:
718:
697:
696:
676:
675:
652:
651:
632:(7): 359–367,
620:
619:
610:
609:
598:
595:
592:
591:
588:
584:
583:
580:
576:
575:
572:
568:
567:
564:
560:
559:
556:
552:
551:
548:
544:
543:
540:
536:
535:
532:
528:
527:
524:
520:
519:
516:
512:
511:
508:
501:
498:
495:
494:
491:
490:15 159 089 098
488:
485:
482:
479:
476:
473:
470:
467:
464:
460:
459:
456:
453:
450:
447:
444:
441:
438:
435:
432:
429:
425:
424:
421:
418:
415:
412:
409:
406:
403:
400:
397:
394:
390:
389:
388:6 138 320 000
386:
383:
380:
377:
374:
371:
368:
365:
362:
359:
355:
354:
353:1 828 915 200
351:
348:
345:
342:
339:
336:
333:
330:
327:
324:
320:
319:
316:
313:
310:
307:
304:
301:
298:
295:
292:
289:
285:
284:
281:
278:
275:
272:
269:
266:
263:
260:
257:
254:
250:
249:
246:
243:
240:
237:
234:
231:
228:
225:
222:
219:
215:
214:
211:
208:
205:
202:
199:
196:
193:
190:
187:
184:
180:
179:
176:
173:
170:
167:
164:
161:
158:
155:
152:
149:
145:
144:
141:
138:
135:
132:
129:
126:
123:
120:
117:
114:
110:
109:
106:
103:
100:
97:
94:
91:
88:
85:
82:
79:
75:
74:
71:
68:
65:
62:
59:
56:
53:
50:
47:
44:
41:
38:
32:
29:
13:
10:
9:
6:
4:
3:
2:
768:
757:
754:
753:
751:
741:
738:
735:
732:
730:online table.
729:
726:
725:
721:
715:
711:
704:
699:
698:
693:
686:
682:
681:Miller, Mirka
678:
677:
672:
667:
663:
659:
654:
653:
649:
645:
640:
635:
631:
627:
622:
621:
617:
612:
611:
606:
601:
600:
596:
589:
586:
585:
581:
578:
577:
573:
570:
569:
565:
562:
561:
557:
554:
553:
549:
546:
545:
541:
538:
537:
533:
530:
529:
525:
522:
521:
517:
514:
513:
509:
506:
505:
500:Key to colors
499:
492:
489:
487:1 154 305 152
486:
483:
480:
477:
474:
471:
468:
465:
462:
461:
457:
455:6 899 904 000
454:
451:
448:
445:
442:
439:
436:
433:
430:
427:
426:
422:
420:2 910 897 000
419:
416:
413:
410:
407:
404:
401:
398:
395:
392:
391:
387:
385:1 119 744 000
384:
381:
378:
375:
372:
369:
366:
363:
360:
357:
356:
352:
349:
346:
343:
340:
337:
334:
331:
328:
325:
322:
321:
317:
314:
311:
308:
305:
302:
299:
296:
293:
290:
287:
286:
282:
279:
276:
273:
270:
267:
264:
261:
258:
255:
252:
251:
247:
244:
241:
238:
235:
232:
229:
226:
223:
220:
217:
216:
212:
209:
206:
203:
200:
197:
194:
191:
188:
185:
182:
181:
177:
174:
171:
168:
165:
162:
159:
156:
153:
150:
147:
146:
142:
139:
136:
133:
130:
127:
124:
121:
118:
115:
112:
111:
107:
104:
101:
98:
95:
92:
89:
86:
83:
80:
77:
76:
72:
69:
66:
63:
60:
57:
54:
51:
48:
45:
37:
36:
30:
28:
26:
22:
19:
713:
709:
691:
661:
657:
639:math/9504214
629:
625:
615:
604:
318:457 228 800
283:113 799 168
15:
664:(1): 1–12,
484:121 080 960
452:588 931 200
417:282 268 800
382:125 452 800
350:384 072 192
315:113 799 168
248:27 783 000
740:Eyal Loz's
597:References
481:17 297 280
449:58 893 120
414:31 152 000
379:15 681 600
347:50 803 200
312:18 289 152
280:27 783 000
213:5 184 000
607:: 249–272
478:2 162 160
446:8 648 640
443:1 235 520
411:3 991 680
376:1 960 200
344:7 257 600
341:1 036 800
309:3 048 192
277:5 644 800
274:1 128 960
245:5 184 000
242:1 411 200
210:1 010 658
750:Category
626:Networks
510:Details
178:648 000
21:digraphs
716:: 63–80
475:240 240
440:154 440
408:665 280
373:332 640
338:151 200
306:508 032
271:225 792
239:352 800
207:259 200
175:137 370
143:41 472
472:24 024
437:17 160
405:95 040
402:11 880
370:55 400
335:30 240
303:60 480
300:15 120
268:20 160
236:88 200
204:86 400
201:28 800
172:42 309
169:14 400
140:11 568
706:(PDF)
688:(PDF)
634:arXiv
507:Color
469:2 184
434:1 716
399:1 320
367:7 920
332:5 040
297:3 024
265:6 720
262:1 680
233:9 020
230:2 520
198:3 775
195:1 152
166:7 200
163:1 378
137:5 115
134:2 041
131:1 152
108:737
666:doi
644:doi
466:182
463:13
431:156
428:12
396:132
393:11
364:990
361:110
358:10
329:720
294:504
259:336
227:840
224:210
192:360
189:120
160:465
157:168
128:333
125:165
105:504
102:336
99:171
96:144
73:11
752::
714:41
712:,
708:,
690:,
662:58
660:,
642:,
630:24
628:,
326:90
323:9
291:72
288:8
256:56
253:7
221:42
218:6
186:30
183:5
154:60
151:20
148:4
122:60
119:27
116:12
113:3
93:72
90:27
87:20
84:10
78:2
70:10
736:.
668::
646::
636::
587:*
579:*
571:*
563:*
555:*
547:*
539:*
531:*
523:*
515:*
81:6
67:9
64:8
61:7
58:6
55:5
52:4
49:3
46:2
42:d
39:k
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.