New record graphs in the degree-diameter problem

Loz, Eyal and Siran, Jozef (2008). New record graphs in the degree-diameter problem. Australasian Journal of Combinatorics, 41 pp. 63–80.

URL: http://ajc.maths.uq.edu.au/pdf/41/ajc_v41_p063.pdf

Abstract

In 1994, Dinneen and Hafner (Networks 24 No. 7, 359–367) published a table of largest orders of graphs of given degree up to 15 and diameter up to 10, known to that date. The table also contained 48 new values found by the authors with the help of computer searches over Cayley graphs of semidirect products of (mostly) cyclic groups. Prior to our work, only relatively few values in the table have been improved; updates have been maintained on the web. With the help of voltage graphs in combination with random computer search we have substantially improved more than half of the values in (all earlier updates of) the table.

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