29:
598:
466:
853:. Colloques internationaux du Centre National de la Recherche Scientifique. Vol. 260. Éditions du Centre national de la recherche scientifique. pp. 35–38.
888:
858:
817:
180:
725:
757:
Ge, G.; Miao, Y.; Sun, X. (2010). "Perfect difference families, perfect difference matrices, and related combinatorial structures".
713:
292:
1 because its central vertex is an articulation point; however, like the complete graphs from which it is formed, it is
399:
681:
Koh, K. M.; Rogers, D. G.; Teo, H. K.; Yap, K. Y. (1980). "Graceful graphs: some further results and problems".
289:
893:
301:
105:
95:
43:
390:
115:
343:
62:
851:
Problèmes combinatoires et théorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976)
782:
812:. Colloquia mathematica Societatis János Bolyai. Vol. 18. North-Holland. pp. 135–149.
854:
813:
739:
721:
657:
484:
766:
369:
325:
244:
212:
131:
868:
827:
778:
735:
694:
642:
864:
842:
823:
774:
731:
690:
638:
376:
357:
143:
619:
234:
28:
882:
786:
509:. Through an equivalence with perfect difference families, this has been proved for
393:
can be deduced from the chromatic polynomial of the complete graph and is equal to
801:
660:
517:
193:
846:
805:
709:
305:
189:
623:
597:
248:
743:
718:
Graph theory and combinatorics (Proc. Conf., Open Univ., Milton Keynes, 1978)
665:
720:. Research notes in mathematics. Vol. 34. Pitman. pp. 18–37.
810:
Combinatorics (Proc. Fifth
Hungarian Colloq., Keszthely, 1976), Vol. I
770:
596:
16:
Graph family made by joining complete graphs at a universal node
806:"On a combinatorial problem of antennas in radioastronomy"
710:"Graceful graphs, radio antennae and French windmills"
402:
161:
142:
130:
114:
104:
94:
61:
42:
21:
460:
847:"Systèmes de triplets et différences associées"
461:{\displaystyle x\prod _{i=1}^{k-1}(x-i)^{n}.}
8:
494:. In 1979, Bermond has conjectured that
449:
421:
410:
401:
611:
808:. In Hajnal, A.; Sos, Vera T. (eds.).
18:
7:
624:"A dynamic survey of graph labeling"
316:By construction, the windmill graph
631:Electronic Journal of Combinatorics
288:), radius 1 and diameter 2. It has
14:
759:Journal of Combinatorial Designs
27:
446:
433:
181:Table of graphs and parameters
1:
889:Parametric families of graphs
575:is graceful if and only if
910:
520:, and Turgeon proved that
251:of these complete graphs.
179:
26:
708:Bermond, J.-C. (1979).
368:The windmill graph has
352:and the windmill graph
300:-edge-connected. It is
804:; Turgeon, J. (1978).
683:Congressus Numerantium
602:
601:Small windmill graphs.
462:
432:
364:Labeling and colouring
600:
532:is not graceful when
463:
406:
334:, the windmill graph
845:; Germa, A. (1978).
502:is graceful for all
400:
391:chromatic polynomial
471:The windmill graph
290:vertex connectivity
281:edges, girth 3 (if
247:. That is, it is a
33:The Windmill graph
658:Weisstein, Eric W.
622:(3 January 2007).
603:
458:
860:978-2-222-02070-7
819:978-0-444-85095-9
771:10.1002/jcd.20259
302:trivially perfect
215:constructed for
186:
185:
901:
873:
872:
841:Bermond, J.-C.;
838:
832:
831:
800:Bermond, J.-C.;
797:
791:
790:
754:
748:
747:
714:Wilson, Robin J.
705:
699:
698:
678:
672:
671:
670:
661:"Windmill Graph"
653:
647:
646:
628:
616:
588:
581:
574:
566:
559:
552:
545:
538:
531:
515:
508:
501:
493:
482:
467:
465:
464:
459:
454:
453:
431:
420:
388:
374:
370:chromatic number
355:
351:
341:
333:
326:friendship graph
323:
299:
287:
280:
269:
245:universal vertex
242:
232:
228:
221:
213:undirected graph
210:
175:
157:
138:
132:Chromatic number
126:
90:
89:
87:
86:
83:
80:
57:
36:
31:
19:
909:
908:
904:
903:
902:
900:
899:
898:
879:
878:
877:
876:
861:
840:
839:
835:
820:
799:
798:
794:
756:
755:
751:
728:
707:
706:
702:
680:
679:
675:
656:
655:
654:
650:
626:
618:
617:
613:
608:
595:
583:
576:
568:
567:. The windmill
561:
554:
547:
540:
533:
521:
510:
503:
495:
488:
472:
445:
398:
397:
379:
377:chromatic index
372:
366:
358:butterfly graph
353:
350:
346:
335:
332:
328:
317:
314:
293:
282:
271:
260:
257:
241:
237:
230:
223:
216:
200:
165:
148:
144:Chromatic index
136:
121:
84:
81:
71:
70:
68:
67:
48:
38:
34:
17:
12:
11:
5:
907:
905:
897:
896:
894:Perfect graphs
891:
881:
880:
875:
874:
859:
843:Brouwer, A. E.
833:
818:
792:
765:(6): 415–449.
749:
727:978-0273084358
726:
700:
673:
648:
620:Gallian, J. A.
610:
609:
607:
604:
594:
591:
483:is proved not
469:
468:
457:
452:
448:
444:
441:
438:
435:
430:
427:
424:
419:
416:
413:
409:
405:
365:
362:
348:
330:
313:
310:
256:
253:
239:
235:complete graph
233:copies of the
198:windmill graph
184:
183:
177:
176:
163:
159:
158:
146:
140:
139:
134:
128:
127:
118:
112:
111:
108:
102:
101:
98:
92:
91:
65:
59:
58:
46:
40:
39:
32:
24:
23:
22:Windmill graph
15:
13:
10:
9:
6:
4:
3:
2:
906:
895:
892:
890:
887:
886:
884:
870:
866:
862:
856:
852:
848:
844:
837:
834:
829:
825:
821:
815:
811:
807:
803:
796:
793:
788:
784:
780:
776:
772:
768:
764:
760:
753:
750:
745:
741:
737:
733:
729:
723:
719:
715:
711:
704:
701:
696:
692:
688:
684:
677:
674:
668:
667:
662:
659:
652:
649:
644:
640:
636:
632:
625:
621:
615:
612:
605:
599:
592:
590:
586:
579:
572:
564:
557:
550:
543:
536:
529:
525:
519:
513:
506:
499:
491:
486:
480:
476:
455:
450:
442:
439:
436:
428:
425:
422:
417:
414:
411:
407:
403:
396:
395:
394:
392:
386:
382:
378:
371:
363:
361:
359:
345:
339:
327:
321:
312:Special cases
311:
309:
307:
303:
297:
291:
285:
278:
274:
270:vertices and
267:
263:
254:
252:
250:
246:
236:
226:
219:
214:
208:
204:
199:
195:
191:
182:
178:
173:
169:
164:
160:
155:
151:
147:
145:
141:
135:
133:
129:
124:
119:
117:
113:
109:
107:
103:
99:
97:
93:
78:
74:
66:
64:
60:
55:
51:
47:
45:
41:
30:
25:
20:
850:
836:
809:
795:
762:
758:
752:
717:
703:
686:
682:
676:
664:
651:
634:
630:
614:
584:
577:
570:
562:
555:
548:
541:
534:
527:
523:
511:
504:
497:
489:
478:
474:
470:
384:
380:
367:
337:
319:
315:
295:
283:
276:
272:
265:
261:
258:
249:1-clique-sum
243:at a shared
224:
217:
206:
202:
197:
194:graph theory
190:mathematical
187:
171:
167:
153:
149:
122:
76:
72:
53:
49:
689:: 559–571.
587:≡ 1 (mod 4)
580:≡ 0 (mod 4)
553:, and when
516:. Bermond,
306:block graph
229:by joining
883:Categories
802:Kotzig, A.
606:References
344:star graph
255:Properties
787:120800012
744:757210583
666:MathWorld
440:−
426:−
408:∏
192:field of
637:: 1–58.
485:graceful
268:– 1) + 1
162:Notation
106:Diameter
56:– 1) + 1
44:Vertices
869:0539936
828:0519261
779:2743134
736:0587620
716:(ed.).
695:0608456
643:1668059
593:Gallery
356:is the
354:Wd(3,2)
342:is the
324:is the
259:It has
188:In the
88:
69:
35:Wd(5,4)
867:
857:
826:
816:
785:
777:
742:
734:
724:
693:
641:
518:Kotzig
514:≤ 1000
492:> 5
389:. Its
304:and a
286:> 2
279:− 1)/2
211:is an
196:, the
125:> 2
96:Radius
783:S2CID
712:. In
627:(PDF)
569:Wd(3,
496:Wd(4,
336:Wd(2,
318:Wd(3,
120:3 if
116:Girth
63:Edges
855:ISBN
814:ISBN
740:OCLC
722:ISBN
560:and
539:and
387:– 1)
375:and
298:– 1)
222:and
156:– 1)
79:− 1)
767:doi
635:DS6
582:or
565:= 2
558:= 5
551:= 3
546:or
544:= 2
537:= 4
522:Wd(
507:≥ 4
487:if
473:Wd(
227:≥ 2
220:≥ 2
201:Wd(
166:Wd(
885::
865:MR
863:.
849:.
824:MR
822:.
781:.
775:MR
773:.
763:18
761:.
738:.
732:MR
730:.
691:MR
687:29
685:.
663:.
639:MR
633:.
629:.
589:.
360:.
308:.
273:nk
73:nk
871:.
830:.
789:.
769::
746:.
697:.
669:.
645:.
585:n
578:n
573:)
571:n
563:n
556:k
549:n
542:n
535:k
530:)
528:n
526:,
524:k
512:n
505:n
500:)
498:n
490:k
481:)
479:n
477:,
475:k
456:.
451:n
447:)
443:i
437:x
434:(
429:1
423:k
418:1
415:=
412:i
404:x
385:k
383:(
381:n
373:k
349:n
347:S
340:)
338:n
331:n
329:F
322:)
320:n
296:k
294:(
284:k
277:k
275:(
266:k
264:(
262:n
240:k
238:K
231:n
225:n
218:k
209:)
207:n
205:,
203:k
174:)
172:n
170:,
168:k
154:k
152:(
150:n
137:k
123:k
110:2
100:1
85:2
82:/
77:k
75:(
54:k
52:(
50:n
37:.
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