Table of the orders of the largest known regular toroidal graphs for the undirected degree diameter problem
\ 
2 
3 
4 
5 
6 
7 
8

3 
10 
16 
26 
38 
56 
74 
92

4 
13 
25 
41 
61 
85 
134 
243

5 
16 
30 
48 
70 
124 
254 
500

6 
19 
37 
61 
91 
127 
169 
217

Optimal graphs are marked in bold. The following table is the key to the colors in the table presented above:
Color 
Details

* 
The Petersen graph.

* 
Graphs found by Preen. Details are available in a paper by the author.

* 
Regular planar graphs.

Table of the orders of the largest known toroidal graphs for the undirected degree diameter problem
\ 
2 
3 
4 
5 
6 
7 
8 
9 
10

3 
10 
16 
26 
38 
56 
74 
92 
120 
160

4 
13 
25 
41 
61 
90 
180 
270 
540 
810

5 
16 
30 
48 
100 
160 
400 
640 
1600 
2560

6 
19 
37 
61 
150 
280 
750 
1405 
3750 
7030

7 
12 
35 
74 
210 
452 
1260 
2720 
7560 
16328

8 
13 
40 
97 
280 
685 
1960 
4901 
13720 
33613

9 
14 
45 
122 
364 
986 
2884 
7898 
23044 
63194

10 
16 
50 
151 
476 
1366 
4256 
12301 
38276 
110716

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

* 
Regular toroidal graphs.

* 
Planar graphs.

* 
Graphs found by R. FeriaPurón and G. PinedaVillavicencio. Details are available in a paper by the authors.

References
 FeriaPurón, R.; PinedaVillavicencio, G. (2013), "Constructions of large graphs on surfaces", preprint, PDF version.
 Preen, J. (2010), "Largest 6regular toroidal graphs for a given diameter", The Australasian Journal of Combinatorics 47:5357.
 Tishchenko, S. A. (2001), "The largest graphs of diameter 2 and fixed Euler characteristics", Fundam. Prikl. Mat., 7:12031225.
External links