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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)