论文标题
伪几何强烈规则的图形
Pseudo-Geometric Strongly Regular Graphs with a Regular Point
论文作者
论文摘要
我们研究了伪几何强烈规则的图形，其第二个子基础相对于顶点是强烈的图形或完整图的封面。通过研究此类图的结构，我们表征了所有包含此类顶点的图形，并使用我们的表征来找到许多新的强烈规则图。因此，我们回答了Gardiner，Godsil，Hensel和Royle提出的一个问题。我们为Q新的，成对的非同构图提供了明确的结构，其参数与订单$（Q，Q）$的通用四边形的共线性图相同，并且具有与Hermitian广义Quadrange Quadrange Quadrange Quadrange Quadrange $（Q^2，Q^2，Q）$ QUERS $ QUERS $ QUERS $ QUERS $ QUERS $ QUERS $ QUERS QUERS，Q $ QUers PRIME的新的非几何图。使用我们的表征，我们计算了具有参数（85,20,3,5）的135478新的强度定期图和27 039个具有参数（156、30、30、4、6）的强烈规则图。
We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs containing such a vertex, and use our characterization to find many new strongly regular graphs. Thereby, we answer a question posed by Gardiner, Godsil, Hensel, and Royle. We give an explicit construction for q new, pairwise non-isomorphic graphs with the same parameters as the collinearity graph of generalized quadrangles of order $(q,q)$ and a new non-geometric graph with the same parameters as the collinearity graph of the Hermitian generalized quadrangle of order $(q^2, q)$, for prime powers $q$. Using our characterization, we computed 135478 new strongly regular graphs with parameters (85,20,3,5) and 27 039 strongly regular graphs with parameters (156, 30, 4, 6).
