星图的张成直径

7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings. Pub Date : 2004-05-10 DOI:10.1109/ISPAN.2004.1300536

Cheng-Kuan Lin, Hua-Min Huang, D. Hsu, Lih-Hsing Hsu

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引用次数: 6

摘要

设u和v是S/sub n/的n/ spl ges/ 5的不同部集的任意两个不同的顶点。我们证明了存在(n - 1)条内部不相交路径P/下标1/，P/下标2/，…， P/下标n-i/将u与v连接，使得/spl cup//sup n = 1//下标i = 2/ P/下标i/跨出S/下标n/和l(P/下标i/) /spl les/ (n - 1)!+ 2(n - 2)!+ 2(n - 3)!+ 1 = n!/(n - 2) + 1。我们还证明了有两条内部不相交的路径Q/下标1/和Q/下标2/连接u和v，使得Q/下标1/ /spl cup/ Q/下标2/跨越S/下标n/和l(Q/下标i/) /spl les/ n!/2 + l对于I = 1,2。

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The spanning diameter of the star graphs

Assume that u and v are any two distinct vertices of different partite sets of S/sub n/ with n /spl ges/ 5. We prove that there are (n - 1) internally disjoint paths P/sub 1/, P/sub 2/, ..., P/sub n-i/ joining u to v such that /spl cup//sup n = 1//sub i = 2/ P/sub i/ spans S/sub n/ and l(P/sub i/) /spl les/ (n - 1)! + 2(n - 2)! + 2(n - 3)! + 1 = n!/(n - 2) + 1. We also prove that there are two internally disjoint paths Q/sub 1/ and Q/sub 2/ joining u to v such that Q/sub 1/ /spl cup/ Q/sub 2/ spans S/sub n/ and l(Q/sub i/) /spl les/ n!/2 + l for i = 1,2.

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7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings.

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