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'''Table of the orders of the largest known vertex symmetric graphs for the directed Degree Diameter problem:'''
{{Navbox
| name = InuYasha
| title = ''[[InuYasha]]'' by [[Rumiko Takahashi]]


<center>
| group1 = Franchise
{| border="1" cellspacing="2" cellpadding="2" style="text-align: center;"
| list1 = [[List of InuYasha chapters|Chapters]]{{•}} [[List of InuYasha episodes|Episodes]]{{•}} [[List of InuYasha locations|Locations]]{{•}} [[List of InuYasha terms|Terms]]{{•}} ''[[InuYasha the Movie: Affections Touching Across Time|Affections Touching Across Time]]''{{•}} ''[[InuYasha the Movie: The Castle Beyond the Looking Glass|Castle Beyond the Looking Glass]]''{{•}} ''[[InuYasha the Movie: Swords of an Honorable Ruler|Swords of an Honorable Ruler]]''{{•}} ''[[InuYasha the Movie: Fire on the Mystic Island|Fire on the Mystic Island]]''
| '''d\k'''|| '''2''' || '''3''' || '''4'''|| '''5''' || '''6''' || '''7''' || '''8''' || '''9''' || '''10''' || '''11'''
|-
| '''2''' ||style="background-color: blue;" | 6 ||style="background-color: #99FF00;" | 10 ||style="background-color: #FF0033;" | 20 ||style="background-color: #FF0033;" | 27 ||style="background-color: #663333;" | 72 ||style="background-color: #663333;" | 144 ||style="background-color: #99FF00;" | 171 ||style="background-color: #6666CC;" | 336 ||style="background-color: #6666CC;" | 504 ||style="background-color: #99FF00;" | 737
|-
| '''3''' ||style="background-color: blue;" | 12 ||style="background-color: #FF0033;" | 27 ||style="background-color: #669999;" | 60 ||style="background-color: #666633;" | 165 || style="background-color: #99FF00;" |333 ||style="background-color: #990099;" | 1 152 ||style="background-color: #FF9900;" | 2 041 ||style="background-color: #FF9900;" | 5 115 ||style="background-color: #FF9900;" | 11 568 ||style="background-color: #990099;" | 41 472
|-
| '''4''' ||style="background-color: blue;" | 20 ||style="background-color: #6666CC;" | 60 ||style="background-color: #663333;" | 168 ||style="background-color: #FF9900;" | 465 ||style="background-color: #FF9900;" | 1 378 ||style="background-color: #990099;" | 7 200 ||style="background-color: #666666;" | 14 400 ||style="background-color: #FF9900;" | 42 309 ||style="background-color: #FF9900;" | 137 370 ||style="background-color: #990099;" | 648 000
|-
| '''5''' ||style="background-color: blue;" | 30 ||style="background-color: #6666CC;" | 120 ||style="background-color: #6666CC;" | 360 ||style="background-color: #990099;" | 1 152 ||style="background-color: #FF9900;" | 3 775 ||style="background-color: #990099;" | 28 800 ||style="background-color: #666666;" | 86 400 ||style="background-color: #990099;" | 259 200 ||style="background-color: #FF9900;" | 1 010 658 ||style="background-color: #990099;" | 5 184 000
|-
| '''6''' ||style="background-color: blue;" | 42 ||style="background-color: #6666CC;" | 210 ||style="background-color: #6666CC;" | 840 ||style="background-color: #6666CC;" | 2 520 ||style="background-color: #FF9900;" | 9 020 ||style="background-color: #990099;" | 88 200 ||style="background-color: #666666;" | 352 800 ||style="background-color: #990099;" | 1 411 200 ||style="background-color: #990099;" | 5 184 000 ||style="background-color: #990099;" | 27 783 000
|-
| '''7''' ||style="background-color: blue;" | 56 ||style="background-color: #6666CC;" | 336 ||style="background-color: #6666CC;" | 1 680 ||style="background-color: #6666CC;" | 6 720 ||style="background-color: #6666CC;" | 20 160 ||style="background-color: #990099;" | 225 792 ||style="background-color: #666666;" | 1 128 960 ||style="background-color: #990099;" | 5 644 800 ||style="background-color: #990099;" | 27 783 000 ||style="background-color: #990099;" | 113 799 168
|-
| '''8''' ||style="background-color: blue;" | 72 ||style="background-color: #6666CC;" | 504 ||style="background-color: #6666CC;" | 3 024 ||style="background-color: #6666CC;" | 15 120 ||style="background-color: #6666CC;" | 60 480 ||style="background-color: #990099;" | 508 032 ||style="background-color: #666666;" | 3 048 192 ||style="background-color: #990099;" | 18 289 152 ||style="background-color: #990099;" | 113 799 168 ||style="background-color: #990099;" | 457 228 800
|-
| '''9''' ||style="background-color: blue;" | 90 ||style="background-color: #6666CC;" | 720 ||style="background-color: #6666CC;" | 5 040 ||style="background-color: #6666CC;" | 30 240 ||style="background-color: #6666CC;" | 151 200 ||style="background-color: #990099;" | 1 036 800 ||style="background-color: #666666;" | 7 257 600 ||style="background-color: #990099;" | 50 803 200 ||style="background-color: #990099;" | 384 072 192 ||style="background-color: #990099;" | 1 828 915 200
|-
| '''10''' ||style="background-color: blue;" | 110 ||style="background-color: #6666CC;" | 990 ||style="background-color: #6666CC;" | 7 920 ||style="background-color: #6666CC;" | 55 400 ||style="background-color: #6666CC;" | 332 640 ||style="background-color: #990099;" | 1 960 200 ||style="background-color: #666666;" | 15 681 600 ||style="background-color: #990099;" | 125 452 800 ||style="background-color: #990099;" | 1 119 744 000 ||style="background-color: #990099;" | 6 138 320 000
|-
| '''11''' ||style="background-color: blue;" | 132 ||style="background-color: #6666CC;" | 1 320 ||style="background-color: #6666CC;" | 11 880 ||style="background-color: #6666CC;" | 95 040 ||style="background-color: #6666CC;" | 665 280 ||style="background-color: #6666CC;" | 3 991 680 ||style="background-color: #666666;" | 31 152 000 ||style="background-color: #990099;" | 282 268 800 ||style="background-color: #990099;" | 2 910 897 000 ||style="background-color: #990099;" | 18 065 203 200
|-
| '''12''' ||style="background-color: blue;" | 156 ||style="background-color: #6666CC;" | 1 716 ||style="background-color: #6666CC;" | 17 160 ||style="background-color: #6666CC;" | 154 440 ||style="background-color: #6666CC;" | 1 235 520 ||style="background-color: #6666CC;" | 8 648 640 ||style="background-color: #666666;" | 58 893 120 ||style="background-color: #990099;" | 588 931 200 ||style="background-color: #990099;" | 6 899 904 000 ||style="background-color: #990099;" | 47 703 427 200
|-
| '''13''' ||style="background-color: blue;" | 182 ||style="background-color: #6666CC;" | 2 184 ||style="background-color: #6666CC;" | 24 024 ||style="background-color: #6666CC;" | 240 240 ||style="background-color: #6666CC;" | 2 162 160 ||style="background-color: #6666CC;" | 17 297 280 ||style="background-color: #6666CC;" | 121 080 960 ||style="background-color: #990099;" | 1 154 305 152 ||style="background-color: #990099;" | 15 159 089 098 ||style="background-color: #990099;" | 115 430 515 200
|}
</center>


| group2 = [[List of InuYasha characters|Characters]]
| list2 = [[InuYasha (character)|InuYasha]]{{•}} [[Kagome Higurashi]]{{•}} [[Myoga (InuYasha)|Myoga]]{{•}} [[Shippo]]{{•}} [[Miroku (InuYasha)|Miroku]]{{•}} [[Sango (InuYasha)|Sango]]{{•}} [[Kirara (InuYasha)|Kirara]]{{•}} [[Koga (InuYasha)|Koga]]{{•}} [[Sesshomaru]]{{•}} [[Jaken]]{{•}} [[Rin (InuYasha)|Rin]]{{•}} [[Kohaku (InuYasha)|Kohaku]]<br>[[Naraku]] ([[Naraku's Offspring|Offspring]]){{•}} [[Kagura (InuYasha)|Kagura]]{{•}} [[Abi-Hime]]{{•}} [[Mōryōmaru]]<br>[[Inu no Taishou]]{{•}} [[Izayoi]]{{•}} [[Ryūkotsusei]]{{•}} [[Menomaru]]{{•}} [[Hyoga]]{{•}} [[Hosenki (InuYasha)|Hosenki]]{{•}} [[Sesshomaru's Mother]]{{•}} [[Kikyo]]{{•}} [[Kaede (InuYasha)|Kaede]]{{•}} [[Tōtōsai]]{{•}} [[Four War Gods]]{{•}} [[Utsugi]]{{•}} [[Band of Seven]]{{•}} [[Hakushin]]{{•}} [[Jinenji]]{{•}} [[Shako (InuYasha)|Shako]]


The following table is the key to the colors in the table presented above:
| group3 = Games
| list3 = ''[[InuYasha: A Feudal Fairy Tale|A Feudal Fairy Tale]]''{{•}} ''[[InuYasha: Feudal Combat|Feudal Combat]]''{{•}} ''[[InuYasha: The Secret of the Cursed Mask|The Secret of the Cursed Mask]]''{{•}} ''[[InuYasha: Secret of the Divine Jewel|Secret of the Divine Jewel]]''


<center>
| group4 = Objects
{| border="1" cellspacing="1" cellpadding="1" style="text-align: left;"
| list4 = [[Dakki]]{{•}} [[Jewel of Four Souls]]
|'''Color''' || style="text-align: center;" |'''Details'''
}}<noinclude>
|-
[[Category:InuYasha| InuYasha]]
|style="background-color: blue; text-align: center;" | * || Family of digraphs found by W.H.Kautz. More details are available in a paper by the author.
[[Category:Anime and manga navigational boxes|InuYasha]]
|-
</noinclude>
|style="background-color: #6666CC; text-align: center;" | * || Family of digraphs found by V.Faber and J.W.Moore. More details are available also by other authors.
|-
|style="background-color: #669999; text-align: center;" | * || Digraph found by V.Faber and J.W.Moore. The complete set of cayley digraphs in that order was found by Eyal Loz.
|-
|style="background-color: #990099; text-align: center;" | * || Digraphs found by Francesc Comellas and M. A. Fiol. More details are available in a paper by the authors.
|-
|style="background-color: #99FF00; text-align: center;" | * || Cayley digraphs found by Michael J. Dinneen. Details about this graph are available in a paper by the author.
|-
|style="background-color: #FF0033; text-align: center;" | * || Cayley digraphs found by Michael J. Dinneen. The complete set of cayley digraphs in that order was found by Eyal Loz.
|-
|style="background-color: #663333; text-align: center;" | * || Cayley digraphs found by Paul Hafner. Details about this graph are available in a paper by the author.
|-
|style="background-color: #666633; text-align: center;" | * || Cayley digraph found by Paul Hafner. The complete set of cayley digraphs in that order was found by Eyal Loz.
|-
|style="background-color: #666666; text-align: center;" | * || Digraphs found by J. Gómez.
|-
|style="background-color: #FF9900; text-align: center;" | * || Cayley digraphs found by Eyal Loz. More details are available in a paper by Eyal Loz and Jozef Širáň.
|}
</center>


==References==
* {{citation
| last1 = Kautz
| first1 = W.H.
| title = Design of optimal interconnection networks for multiprocessors
| journal = Architecture and Design of Digital Computers, Nato Advanced Summer Institute
| year = 1969
| pages = 249-272}}

* {{citation
| last1 = Faber
| first1 = V.
| last2 = Moore
| first2 = J.W.
| title = High-degree low-diameter interconnection networks with vertex symmetry:the directed case
| journal = Technical Report LA-UR-88-1051, Los Alamos National Laboratory
| year = 1988}}

* {{citation
| last1 = J. Dinneen
| first1 = Michael
| last2 = Hafner
| first2 = Paul R.
| title = New Results for the Degree/Diameter Problem
| journal = Networks
| volume = 24
| issue = 7
| year = 1994
| pages = 359-367
| url = http://arxiv.org/PS_cache/math/pdf/9504/9504214v1.pdf}}

* {{citation
| last1 = Comellas
| first1 = F.
| last2 = Fiol
| first2 = M.A.
| title = Vertex symmetric digraphs with small diameter
| journal = Discrete Applied Mathematics
| volume = 58
| year = 1995
| pages = 1-12}}

* {{citation
| last1 = Miller
| first1 = Mirka
| last2 = Širáň
| first2 = Jozef
| title = Moore graphs and beyond: A survey of the degree/diameter problem
| journal = Electronic Journal of Combinatorics
| volume = Dynamic survey D
| year = 2005
| url = www.combinatorics.org/Surveys/ds14.ps}}

* {{citation
| last1 = Loz
| first1 = Eyal
| last2 = Širáň
| first2 = Jozef
| title = New record graphs in the degree-diameter problem
| journal = Australasian Journal of Combinatorics
| volume = 41
| year = 2008
| pages = 63-80
| url = http://ajc.maths.uq.edu.au/volume_contents.php3?vol=41}}

==External links==
* [http://maite71.upc.es/grup_de_grafs/table_g.html Vertex-symmetric Digraphs] online table.
* [http://moorebound.indstate.edu/index.php/Main_Page Degree Diameter] self-update wiki.
* [http://www.eyal.tk/degreediameter/ Eyal Loz]'s Degree-Diameter problem page.

Revision as of 10:29, 11 October 2008

Table of the orders of the largest known vertex symmetric graphs for the directed Degree Diameter problem:

d\k 2 3 4 5 6 7 8 9 10 11
2 6 10 20 27 72 144 171 336 504 737
3 12 27 60 165 333 1 152 2 041 5 115 11 568 41 472
4 20 60 168 465 1 378 7 200 14 400 42 309 137 370 648 000
5 30 120 360 1 152 3 775 28 800 86 400 259 200 1 010 658 5 184 000
6 42 210 840 2 520 9 020 88 200 352 800 1 411 200 5 184 000 27 783 000
7 56 336 1 680 6 720 20 160 225 792 1 128 960 5 644 800 27 783 000 113 799 168
8 72 504 3 024 15 120 60 480 508 032 3 048 192 18 289 152 113 799 168 457 228 800
9 90 720 5 040 30 240 151 200 1 036 800 7 257 600 50 803 200 384 072 192 1 828 915 200
10 110 990 7 920 55 400 332 640 1 960 200 15 681 600 125 452 800 1 119 744 000 6 138 320 000
11 132 1 320 11 880 95 040 665 280 3 991 680 31 152 000 282 268 800 2 910 897 000 18 065 203 200
12 156 1 716 17 160 154 440 1 235 520 8 648 640 58 893 120 588 931 200 6 899 904 000 47 703 427 200
13 182 2 184 24 024 240 240 2 162 160 17 297 280 121 080 960 1 154 305 152 15 159 089 098 115 430 515 200


The following table is the key to the colors in the table presented above:

Color Details
* Family of digraphs found by W.H.Kautz. More details are available in a paper by the author.
* Family of digraphs found by V.Faber and J.W.Moore. More details are available also by other authors.
* Digraph found by V.Faber and J.W.Moore. The complete set of cayley digraphs in that order was found by Eyal Loz.
* Digraphs found by Francesc Comellas and M. A. Fiol. More details are available in a paper by the authors.
* Cayley digraphs found by Michael J. Dinneen. Details about this graph are available in a paper by the author.
* Cayley digraphs found by Michael J. Dinneen. The complete set of cayley digraphs in that order was found by Eyal Loz.
* Cayley digraphs found by Paul Hafner. Details about this graph are available in a paper by the author.
* Cayley digraph found by Paul Hafner. The complete set of cayley digraphs in that order was found by Eyal Loz.
* Digraphs found by J. Gómez.
* Cayley digraphs found by Eyal Loz. More details are available in a paper by Eyal Loz and Jozef Širáň.


References

  • Kautz, W.H. (1969), "Design of optimal interconnection networks for multiprocessors", Architecture and Design of Digital Computers, Nato Advanced Summer Institute: 249–272
  • Faber, V.; Moore, J.W. (1988), "High-degree low-diameter interconnection networks with vertex symmetry:the directed case", Technical Report LA-UR-88-1051, Los Alamos National Laboratory
  • Comellas, F.; Fiol, M.A. (1995), "Vertex symmetric digraphs with small diameter", Discrete Applied Mathematics, 58: 1–12
  • Miller, Mirka; Širáň, Jozef (2005), [www.combinatorics.org/Surveys/ds14.ps "Moore graphs and beyond: A survey of the degree/diameter problem"], Electronic Journal of Combinatorics, Dynamic survey D {{citation}}: Check |url= value (help)

External links

Retrieved from "https://en.wikipedia.org/w/index.php?title=Template:Inuyasha&oldid=244545558"