论文标题
在新的记录图上，靠近两分的摩尔图
On new record graphs close to bipartite Moore graphs
论文作者
论文摘要
通过图对互连网络进行建模激发了一些极端问题的研究，这些问题涉及图的众所周知的参数（程度，直径，周长和秩序），并要求其中一个固定其他两个固定时，要求其中一个的最佳值。在这里，我们将重点集中在{\ em二分的摩尔图\/}中，也就是说，达到最佳顺序的双分式图，修复了度/直径或度数/周长。两分摩尔图的事实表明，双方摩尔结合所隐含的某些约束。首先，我们处理{\ em local bipartite moore图}。在某些情况下，我们发现那些局部两分的摩尔图与局部周长尽可能近，与双方摩尔图给出的本地腰围。其次，我们构建了一个$（Q+2）$ - 订单$ 2（q^2+Q+5）$和直径$ 3 $的家庭（$ q $ a prime的功率）。这些图达到了$ q = 9 $的记录值，并提高了$ q = 11 $和$ q = 13 $的值。
The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and ask for the optimal value of one of them while holding the other two fixed. Here we focus in {\em bipartite Moore graphs\/}, that is, bipartite graphs attaining the optimum order, fixed either the degree/diameter or degree/girth. The fact that there are very few bipartite Moore graphs suggests the relaxation of some of the constraints implied by the bipartite Moore bound. First we deal with {\em local bipartite Moore graphs}. We find in some cases those local bipartite Moore graphs with local girths as close as possible to the local girths given by a bipartite Moore graph. Second, we construct a family of $(q+2)$-bipartite graphs of order $2(q^2+q+5)$ and diameter $3$, for $q$ a power of prime. These graphs attain the record value for $q=9$ and improve the values for $q=11$ and $q=13$.
