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Exchanged hypercubes [Loh et al., IEEE Transactions on Parallel and Distributed Systems 16 (2005) 866–874] are spanning subgraphs of hypercubes with about one half of their edges but still with many desirable properties of hypercubes. Lower and upper bounds on the domination number of exchanged hypercubes are proved which in particular imply that γ(EH(2,… (More)

This work investigates important properties related to cycles of embedding into the folded hypercube FQ n for n ≥ 2. The authors observe that FQ n is bipartite if and only if n is odd, and show that the minimum length of odd cycles is n + 1 if n is even. The authors further show that every edge of FQ n lies on a cycle of every even length from 4 to 2 n ; if… (More)

As an enhancement on the hypercube Q n , the augmented cube AQ n , proposed by Choudum and Sunitha [S. not only retains some of the favorable properties of Q n but also possesses some embedding properties that Q n does not. For example, AQ n contains cycles of all lengths from 3 to 2 n , but Q n contains only even cycles. In this paper, we obtain two… (More)

The locally twisted cube LTQ n which is a newly introduced interconnection network for parallel computing is a variant of the hypercube Q n. Locally twisted cubes are 4-pancyclic, Applied Mathematics Letters 17 (2004) 919–925] proved that LTQ n is Hamiltonian connected and contains a cycle of length from 4 to 2 n for n ≥ 3. In this work, we improve this… (More)

The super connectivity κ and the super edge-connectivity λ are more refined network reliability indices than connectivity κ and edge-connectivity λ. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), κ (L(G)) = λ (G) if and only if G is not super-λ. As a consequence, we obtain the result of… (More)

As an enhancement on the hypercube Q n , the augmented cube AQ n , prosed by Choudum and Sunitha [S. not only retains some favorable properties of Q n but also possesses some embedding properties that Q n does not. For example, AQ n is pancyclic, that is, AQ n contains cycles of arbitrary length for n 2. This paper shows that AQ n remains pancyclic provided… (More)

The Möbius cube MQ n and the crossed cube CQ n are two important variants of the hypercube Q n. This paper shows that for any two different vertices u and v in G ∈ {MQ n , CQ n } with n 3, there exists a uv-path of every length from d G (u, v) + 2 to 2 n − 1 except for a shortest uv-path, where d G (u, v) is the distance between u and v in G. This result… (More)