621:
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29:
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419:
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620:
425:
588:
175:
290:
222:
The complete list of 10-cages and the proof of minimality was given by Mary R. O'Keefe and Pak Ken Wong. There exist 3 distinct
724:
691:
772:
281:
707:
Pisanski, T.; Boben, M.; Marušič, D.; and Orbanić, A. "The
Generalized Balaban Configurations." Preprint. 2001.
262:
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67:
231:
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235:
208:
47:
740:
Bondy, J. A. and Murty, U. S. R. Graph Theory with
Applications. New York: North Holland, p. 237, 1976.
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107:
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611:
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137:
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570:{\displaystyle \cdot (x^{2}-6)^{2}(x^{2}-5)^{4}(x^{2}-2)^{2}(x^{4}-6x^{2}+3)^{8}.}
184:
160:
28:
668:
708:
414:{\displaystyle (x-3)(x-2)(x-1)^{8}x^{2}(x+1)^{8}(x+2)(x+3)\cdot }
234:. Moreover, the Harries–Wong graph and Harries graph are
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756:. Master Thesis, Universität Tübingen, 2018
721:A smallest graph of girth 10 and valency 3
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215:. Published in 1972, It was the first 10-
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626:Another drawing of the Balaban 10-cage.
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16:Cubic graph with 70 nodes and 105 edges
18:
7:
719:Mary R. O'Keefe and Pak Ken Wong,
14:
614:of the Balaban 10-cage is 3.
598:of the Balaban 10-cage is 2.
219:discovered but it is not unique.
619:
603:
587:
226:-cages, the other two being the
27:
725:Journal of Combinatorial Theory
692:Journal of Combinatorial Theory
688:A trivalent graph of girth ten
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176:Table of graphs and parameters
1:
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284:of the Balaban 10-cage is
211:and 105 edges named after
282:characteristic polynomial
174:
26:
241:The Balaban 10-cage has
754:Linear Layouts with SAT
571:
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263:vertex-connected graph
572:
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684:Alexandru T. Balaban
426:
291:
213:Alexandru T. Balaban
42:Alexandru T. Balaban
33:The Balaban 10-cage
661:Weisstein, Eric W.
567:
411:
232:Harries–Wong graph
773:Individual graphs
664:"Balaban 10-Cage"
261:. It is also a 3-
236:cospectral graphs
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596:chromatic number
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243:chromatic number
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108:Chromatic number
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731:(1980), 91–105.
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641:Balaban 11-cage
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637:Molecular graph
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612:chromatic index
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247:chromatic index
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193:Balaban 10-cage
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118:Chromatic index
34:
22:Balaban 10-cage
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12:
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5:
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778:Regular graphs
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749:Jessica Wolz,
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271:book thickness
267:edge-connected
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138:Book thickness
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273:is 3 and the
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228:Harries graph
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205:regular graph
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98:Automorphisms
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698:(1972), 1–5.
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279:
275:queue number
240:
221:
196:
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189:graph theory
185:mathematical
182:
148:Queue number
751:Engineering
259:hamiltonian
169:Hamiltonian
39:Named after
767:Categories
727:Series B
646:References
257:10 and is
157:Properties
694:Series B
669:MathWorld
533:−
504:−
475:−
446:−
430:⋅
409:⋅
331:−
316:−
301:−
187:field of
632:See also
251:diameter
230:and the
209:vertices
207:with 70
197:Balaban
78:Diameter
48:Vertices
581:Gallery
203:is a 3-
183:In the
277:is 2.
269:. The
265:and 3-
224:(3,10)
199:(3,10)
191:, the
68:Radius
255:girth
201:-cage
161:Cubic
128:Genus
88:Girth
58:Edges
610:The
594:The
280:The
217:cage
165:Cage
253:6,
249:3,
245:2,
195:or
62:105
769::
729:29
723:,
696:12
690:,
686:,
666:.
238:.
102:80
92:10
52:70
710:.
672:.
565:.
560:8
556:)
552:3
549:+
544:2
540:x
536:6
528:4
524:x
520:(
515:2
511:)
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495:x
491:(
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478:5
470:2
466:x
462:(
457:2
453:)
449:6
441:2
437:x
433:(
406:)
403:3
400:+
397:x
394:(
391:)
388:2
385:+
382:x
379:(
374:8
370:)
366:1
363:+
360:x
357:(
352:2
348:x
342:8
338:)
334:1
328:x
325:(
322:)
319:2
313:x
310:(
307:)
304:3
298:x
295:(
152:2
142:3
132:9
122:3
112:2
82:6
72:6
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