On Moore Graphs with Diameters 2 and 3
On Moore Graphs with Diameters 2 and 3
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DOI：
10.1147/rd.45.0497
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发表时间：
1960-11
期刊：
影响因子：
--
通讯作者：
A. Hoffman;R. Singleton
中科院分区：
文献类型：
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作者：
A. Hoffman;R. Singleton
本文讨论了连通无向图的存在性，连通无向图的度为d，直径为k，根据一定的定义，连通无向图的节点数是最大的。对于k = 2，d = 2，3，7和可能d = 57（尚未确定）存在唯一图，但不存在其他度。当k = 3时，一个图只存在于d = 2时。证明利用了图的邻接矩阵（及其主子矩阵）的特征根和特征向量。
This note treats the existence of connected, undirected graphs homogeneous of degree d and of diameter k, having a number of nodes which is maximal according to a certain definition. For k = 2 unique graphs exist for d = 2, 3, 7 and possibly for d = 57 (which is undecided), but for no other degree. For k = 3 a graph exists only for d = 2. The proof exploits the characteristic roots and vectors of the adjacency matrix (and its principal submatrices) of the graph.