Difference between revisions of "The Degree Diameter Problem for Toroidal Graphs"
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Contents
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. 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.