New record graphs in the degree-diameter problem
New record graphs in the degree-diameter problem
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发表时间：
2008
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通讯作者：
Eyal Loz;J. Širáň
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作者：
Eyal Loz;J. Širáň
1994年，Dinneen和Hafner（网络24 No.7, 359-367）发表了当时已知的给定度为15、直径为10的图的最大阶数表。该表还包含48个新值，这些值是作者通过计算机搜索（大部分）环群的半直积的Cayley图发现的。在我们工作之前，该表中只有相对较少的值得到了改进；更新已在网上保持。在电压图与随机计算机搜索相结合的帮助下，我们已经大大改进了该表（所有早期更新）中一半以上的值。
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.