Table of the orders of the largest known regular toroidal graphs for the undirected degree diameter problem
[math]d[/math]\[math]k[/math] |
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
[math]d[/math]\[math]k[/math] |
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. Feria-Purón and G. Pineda-Villavicencio. Details are available in a paper by the authors.
|
References
- Feria-Purón, R.; Pineda-Villavicencio, G. (2013), "Constructions of large graphs on surfaces", preprint, PDF version.
- Preen, J. (2010), "Largest 6-regular toroidal graphs for a given diameter", The Australasian Journal of Combinatorics 47:53-57.
- Tishchenko, S. A. (2001), "The largest graphs of diameter 2 and fixed Euler characteristics", Fundam. Prikl. Mat., 7:1203-1225.
External links