VERTEX-FAULT-TOLERANT CYCLES EMBEDDING ON ENHANCED HYPERCUBE NETWORKS |
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Authors: | Yanjuan ZHANG Hongmei LIU Min LIU |
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Affiliation: | College of Science, China Three Gorges University, Yichang, Hubei Province, 443002, China |
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Abstract: | In this paper, we study the enhanced hypercube, an attractive variant of the hypercube and obtained by adding some complementary edges from a hypercube, and focus on cycles embedding on the enhanced hypercube with faulty vertices. Let Fv be the set of faulty vertices in the n-dimensional enhanced hypercube Qn,k (n ≥ 3, 1 ≤ k ≤ n ? 1). When |Fv| = 2, we showed that Qn,k ? Fv contains a fault-free cycle of every even length from 4 to 2n – 4 where n (n ≥ 3) and k have the same parity; and contains a fault-free cycle of every even length from 4 to 2n ? 4, simultaneously, contains a cycle of every odd length from n ? k + 2 to 2n ? 3 where n (≥ 3) and k have the different parity. Furthermore, when |Fv| = fv ≤ n ? 2, we prove that there exists the longest fault-free cycle, which is of even length 2n ? 2fv whether n (n ≥ 3) and k have the same parity or not; and there exists the longest fault-free cycle, which is of odd length 2n ? 2fv + 1 in Qn,k ? Fv where n (≥ 3) and k have the different parity. |
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Keywords: | enhanced hypercube fault tolerance cycles embedding |
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