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KP 圖


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).

特殊情況總結在下表中。

K_n square P_2 (即,2×n 車圖) 對於所有 n>5 都是不優美的 (Knuth 2024, p. 22)。


另請參閱

Graph Cartesian Product, KC Graph

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參考文獻

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

請引用本文為

Weisstein, Eric W. "KP 圖。" 來自 Web 資源。 https://mathworld.tw/KPGraph.html

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