主题
Search

KP 图


The graph Cartesian product K_n square P_r of a complete graph K_n and a path graph P_r has been termed a "KP graph" by Knuth (2024, pp. 20-21), who restricts their parameters to r>1 and n>2. The KP graphs have vertex count, edge count, and (except for r=1 and r=n=2) graph automorphism count

|V(K_n square P_r)|=rn
(1)
|E(K_n square P_r)|=r(n; 2)+(r-1)n
(2)
|Aut(K_n square P_r)|=2n!.
(3)

KP graphs are regular only for n=1 (corresponding to complete graphs) and n=2 (corresponding to 2×r rook graphs).

特殊情况总结在下表中。

K_n square P_2 (即,2×n 车图) 对于所有 n>5 都是不优美的 (Knuth 2024, p. 22)。


另请参阅

Graph Cartesian Product, KC Graph

使用 探索

参考文献

Knuth, D. E. §7.2.2.3 in The Art of Computer Programming, Vol. 4. 预印本分册 7A, Dec. 5, 2024.

请引用本文为

Weisstein, Eric W. "KP 图。" 来自 Web 资源。 https://mathworld.net.cn/KPGraph.html

主题分类