Table of the orders of the largest known regular planar graphs for the undirected degree diameter problem
[math]d[/math]\[math]k[/math] 
2 
3 
4 
5 
6 
7 
8

3 
6 
12 
18 
28 
36 
52 
76

4 
9 
16 
27 
44 
81 
134 
243

5 
NA 
16 
28 
62 
124 
254 
500

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

* 
Graphs found by Preen.

* 
Graphs found by Pratt and Friedman.

Table of the orders of the largest known planar graphs for the undirected degree diameter problem
[math]d[/math]\[math]k[/math] 
2 
3 
4 
5 
6 
7 
8 
9 
10

3 
7 
12 
18 
28 
38 
53 
77 
109 
157

4 
9 
16 
27 
44 
81 
134 
243 
404 
728

5 
10 
19 
39 
73 
158 
289 
638 
1153 
2558

6 
11 
24 
55 
117 
280 
579 
1405 
2889 
7030

7 
12 
28 
74 
165 
452 
984 
2720 
5898 
16328

8 
13 
33 
97 
228 
685 
1590 
4901 
11124 
33613

9 
14 
37 
122 
293 
986 
2338 
7898 
18698 
63194

10 
16 
42 
151 
375 
1366 
3369 
12301 
30315 
110716

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

* 
Graphs of unknown author.

* 
Graphs found by Fellows, Hell, and Seyffarth. Details are available in a paper by the authors.

* 
Graphs found by Yang, Lin, and Dai. Details are available in a paper by the authors.

* 
Graphs found by Geoffrey Exoo.

* 
Graphs found by S. A. Tishchenko. Details are available in a paper by the author.

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

References
 Fellows, M.; Hell, P.; Seyffarth, K. (1998), "Constructions of large planar networks with given degree and diameter", Networks 32: 275281.
 FeriaPurón, R.; PinedaVillavicencio, G. (2013), "Constructions of large graphs on surfaces", preprint, PDF version.
 Tishchenko, S. A. (2012), "Maximum size of a planar graph with given degree and even diameter", European Journal of Combinatorics 33: 380396.
 Yang, Y.; Lin, J.; Dai, Y. (2002), "Largest planar graphs and largest maximal planar graphs of diameter two", Journal of Computational and Applied Mathematics 144:349358.
External links