Cycles embedding in hypercubes with node failures. Information Processing Letters 作者； Chang-Hsiung Tsai 老師：洪春男 學生 : ：林雨淳. Outline. Introduction Preliminaries Results Conclusions. Introduction. Let f v denote the number of faulty vertices in Q n .
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Information Processing Letters
有 three 4-cycles （100, 110, 111, 101, 100 ）, （010,110, 111, 011, 010 ）, and （101, 111, 011, 001,101 ）
有 Two 6-cycles（100, 110,111, 011, 001, 101, 100 ）and （100, 110, 010, 011, 111,101, 100）
Since Qnis vertex-symmetric , we may assume that the faulty vertex is w = 00 . . . 0. Let e, denoted by (u, v), be a fault-free edge of dimension j , i.e., u = v(j )for 0≦ j≦n−1.
Qnis partitioned along dimension j into two (n − 1)-cubes, denoted by Q0n−1 and Q1n−1, respectively. Hence e is a crossing edge between Q0n−1 and Q1n−1.
By Lemmas 3 and 5, the theorem holds for fv≦ 1. Thus, we only consider the case of 2 ≦ fv ≦n− 2.