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'''NB This page is incomplete and still under construction.'''

===Table of the orders of the largest known arc-transitive graphs for the undirected degree diameter problem===

Below is the table of the largest known arc-transitive graphs in the undirected [[The Degree/Diameter Problem | degree diameter problem]] for graphs of [http://en.wikipedia.org/wiki/Degree_(graph_theory) degree] 3&nbsp;≤&nbsp;''d''&nbsp;≤&nbsp;20 and [http://en.wikipedia.org/wiki/Distance_(graph_theory) diameter] 2&nbsp;≤&nbsp;''k''&nbsp;≤&nbsp;10. All graphs which are known to be optimal are marked in '''bold'''. 

<center> 
{| border="1" cellspacing="2" cellpadding="2" style="text-align: center;"
| '''<math>d</math>\<math>k</math>'''||  '''2''' ||  '''3''' ||  '''4'''|| '''5''' ||  '''6''' || '''7''' ||  '''8''' ||  '''9''' ||  '''10''' 
|-
| '''3''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''4''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''5''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''6''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''7''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''8''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''9''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''10''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''11''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''12''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''13''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''14''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''15''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''16''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''17''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''18''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''19''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
| '''20''' || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 || style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999 ||style="background-color: #eee;" | 999
|-
|}
</center>

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

<center>
{| border="1" cellspacing="1" cellpadding="1" style="text-align: left;"
|'''Color''' || style="text-align: center;" |'''Details'''
|-
|style="background-color: #eee; text-align: center;" | * || Details.
|-
|}
</center>

===Table of the orders of the largest known arc-transitive circulant graphs for the undirected degree diameter problem===

Below is the table of the largest known arc-transitive circulant graphs in the undirected [[The Degree/Diameter Problem | degree diameter problem]] for graphs of [http://en.wikipedia.org/wiki/Degree_(graph_theory) degree] 3&nbsp;≤&nbsp;''d''&nbsp;≤&nbsp;20 and [http://en.wikipedia.org/wiki/Distance_(graph_theory) diameter] 2&nbsp;≤&nbsp;''k''&nbsp;≤&nbsp;10. All graphs which are known to be optimal are marked in '''bold'''. 

<center> 
{| border="1" cellspacing="2" cellpadding="2" style="text-align: center;"
| '''<math>d</math>\<math>k</math>'''||  '''2''' ||  '''3''' ||  '''4'''|| '''5''' ||  '''6''' || '''7''' ||  '''8''' ||  '''9''' ||  '''10''' 
|-
| '''3''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''4''' || style="background-color: #eee;" | 13 || style="background-color: #eee;" | 25 || style="background-color: #eee;" | 41 ||style="background-color: #eee;" | 61 || style="background-color: #eee;" | 85 ||style="background-color: #eee;" | 113 ||style="background-color: #eee;" | 145 ||style="background-color: #eee;" | 181 ||style="background-color: #eee;" | 221
|-
| '''5''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''6''' || style="background-color: #eee;" | 19 || style="background-color: #eee;" | 38 || style="background-color: #eee;" | 117 ||style="background-color: #eee;" | 171 || style="background-color: #eee;" | 279 ||style="background-color: #eee;" | 515 ||style="background-color: #eee;" | 695 ||style="background-color: #eee;" | 905 ||style="background-color: #eee;" | 1393
|-
| '''7''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''8''' || style="background-color: #eee;" | 17 || style="background-color: #eee;" | 75 || style="background-color: #eee;" | 146 ||style="background-color: #eee;" | 401 || style="background-color: #eee;" | 777 ||style="background-color: #eee;" | 1365 ||style="background-color: #eee;" | 2129 ||style="background-color: #eee;" | 3281 ||style="background-color: #eee;" | 5081
|-
| '''9''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''10''' || style="background-color: #eee;" | 41 || style="background-color: #eee;" | 151 || style="background-color: #eee;" | 363 ||style="background-color: #eee;" | 1023 || style="background-color: #eee;" | 1623 ||style="background-color: #eee;" | 4443 ||style="background-color: #eee;" | 6663 ||style="background-color: #eee;" | 11163 ||style="background-color: #eee;" | 18483
|-
| '''11''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''12''' || style="background-color: #eee;" | 57 || style="background-color: #eee;" | 185 || style="background-color: #eee;" | 785 ||style="background-color: #eee;" | 1685 || style="background-color: #eee;" | 3965 ||style="background-color: #eee;" | 10777 ||style="background-color: #eee;" | 15769 ||style="background-color: #eee;" | 35269 ||style="background-color: #eee;" | 52429
|-
| '''13''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''14''' || style="background-color: #eee;" | 71 || style="background-color: #eee;" | 379 || style="background-color: #eee;" | 953 ||style="background-color: #eee;" | 3067 || style="background-color: #eee;" | 8023 ||style="background-color: #eee;" | 18415 ||style="background-color: #eee;" | 37803 ||style="background-color: #eee;" | 72327 ||style="background-color: #eee;" | 196689
|-
| '''15''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''16''' || style="background-color: #eee;" | 97 || style="background-color: #eee;" | 401 || style="background-color: #eee;" | 1649 ||style="background-color: #eee;" | 4947 || style="background-color: #eee;" | 14081 ||style="background-color: #eee;" | 35921 ||style="background-color: #eee;" | 80257 ||style="background-color: #eee;" | 173969 ||style="background-color: #eee;" | 354433
|-
| '''17''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''18''' || style="background-color: #eee;" | ? || style="background-color: #eee;" | ? || style="background-color: #eee;" | 1393 ||style="background-color: #eee;" | ? || style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ?
|-
| '''19''' || style="background-color: #eee;" | - || style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - || style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | - ||style="background-color: #eee;" | -
|-
| '''20''' || style="background-color: #eee;" | 101 || style="background-color: #eee;" | ? || style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? || style="background-color: #eee;" | ? ||style="background-color: #eee;" | 106025 ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ? ||style="background-color: #eee;" | ?
|-
|}
</center>

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

<center>
{| border="1" cellspacing="1" cellpadding="1" style="text-align: left;"
|'''Color''' || style="text-align: center;" |'''Details'''
|-
|style="background-color: #eee; text-align: center;" | * || Details.
|-
|}
</center>