Distance-Regular Graphs of Large Diameter That Are Completely Regular Clique Graphs
Distance-Regular Graphs of Large Diameter That Are Completely Regular Clique Graphs
复制标题
完全正则团图的大直径距离正则图
DOI：
10.1007/s10801-017-0808-9
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Hiroshi Suzuki
中科院分区：
文献类型：
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作者：
Michael E. Hoffman;Kentaro Ihara;Kentaro Ihara;Hirabayashi Mikihito;Hiroshi Suzuki
一个连通图称为参数为（s，c）的完全正则团图，如果存在一个大小为的完全正则团的集合，使得每条边恰好包含在的c个成员中。许多距离正则图族都是完全正则团图。在本文中，我们确定完全正则团图的结构，即，的选择，所有已知的家庭的距离正则图与无界直径。特别地，我们证明了除了Doob图、扭曲Grassmann图和Hermitean形式图之外，这类图中的所有距离正则图都是完全正则团图。我们也确定参数（s，c）;然而，在少数情况下，我们只确定lysand给出了值的界限。我们的结果是一系列工作的推广J. Hemmeter和其他人谁确定的距离正则图在这一类是二分距离正则图的二分之一。
A connected graph is said to be a completely regular clique graph with parameters (s,c),, if there is a collectionof completely regular cliques of sizesuch that every edge is contained in exactlycmembers of. It is known that many families of distance-regular graphs are completely regular clique graphs. In this paper, we determine completely regular clique graph structures, i.e., the choices of, of all known families of distance-regular graphs with unbounded diameter. In particular, we show that all distance-regular graphs in this category are completely regular clique graphs except the Doob graphs, the twisted Grassmann graphs and the Hermitean forms graphs. We also determine parameters (s,c); however, in a few cases we determine onlysand give a bound on the valuec. Our result is a generalization of a series of works by J. Hemmeter and others who determined distance-regular graphs in this category that are bipartite halves of bipartite distance-regular graphs.