Recursive circulants and their embeddings among hypercubes

Park, Jung-Heum; Chwa, Kyung-Yong

doi:10.1016/s0304-3975(00)00176-6

Cited by 66 publications

(34 citation statements)

References 19 publications

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“…Note that each graph in HL m is m-regular and has 2 m vertices. Many well-known interconnection networks are members of HL-graphs including hypercube [17], twisted cube [12], twisted m-cube [9], crossed cube [7], Möbius cube [4], Mcube [25], multiply twisted cube [6], locally twisted cube [28], generalized twisted cube [3], and recursive circulant G(2 m , 4) [20]. There have been many works on the fundamental properties of the above networks such as diameter, connectivity, hamiltonicity, and the embedding of other networks.…”

Section: Preliminariesmentioning

confidence: 99%

The bicube: an interconnection of two hypercubes

Lim

Park

Kim

2014

International Journal of Computer Mathematics

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We consider two definitions of the even-dimensional hypercube given in the literature. The labeled graphs obtained by two definitions are not same, but one is isomorphic to the other. By interconnecting two labeled graphs in such a way that each pair of vertices with the same label are joined by an edge, we construct a vertex-symmetric graph with the diameter about half that of a comparable hypercube. We extend the result to a general scheme for interconnecting two hypercubes to produce a network topology called the bicube. We show that the bicube preserves the vertex-symmetry, bipartiteness, hamiltonian and bipancyclic properties of the hypercube, and is highly edge-symmetric.

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Section: Preliminariesmentioning

confidence: 99%

The bicube: an interconnection of two hypercubes

Lim

Park

Kim

2014

International Journal of Computer Mathematics

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“…In fact, these notions have been investigated in the context of some other networks, for example, in recursive circulant networks [9,24,124], Butterfly networks [25,93,140], cubeconnected cycle networks [58], hypercube-like networks [76,86,123,125], and so on.…”

Section: Remarks and Commentsmentioning

confidence: 99%

Survey on path and cycle embedding in some networks

2009

Front. Math. China

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To find a cycle (resp. path) of a given length in a graph is the cycle (resp. path) embedding problem. To find cycles of all lengths from its girth to its order in a graph is the pancyclic problem. A stronger concept than the pancylicity is the panconnectivity. A graph of order n is said to be panconnected if for any pair of different vertices x and y with distance d there exist xy-paths of every length from d to n. The pancyclicity or the panconnectivity is an important property to determine if the topology of a network is suitable for some applications where mapping cycles or paths of any length into the topology of the network is required. The pancyclicity and the panconnectivity of interconnection networks have attracted much research interest in recent years. A large amount of related work appeared in the literature, with some repetitions. The purpose of this paper is to give a survey of the results related to these topics for the hypercube and some hypercube-like networks.

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“…[1,[4][5][6]9,11,[13][14][15][16][17], which all appeared in Theoretical Computer Science. Almost all known results on this topic for the hypercube and its variations are stated in a survey article by Xu and Ma [20].…”

Section: Introductionmentioning

confidence: 99%

Fault-tolerant panconnectivity of augmented cubes

Wang

2009

Front. Math. China

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The augmented cube AQ n is a variation of the hypercube Q n . This paper considers the panconnectivity of AQ n (n 3) with at most 2n− 5 faulty vertices and/or edges and shows that, for any two fault-free vertices u and v with distance d in AQ n , there exist fault-free uv-paths of every length from d + 2 to 2 n − f − 1, where f is the number of faulty vertices in AQ n . The proof is based on an inductive construction.

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Recursive circulants and their embeddings among hypercubes

Cited by 66 publications

References 19 publications

The bicube: an interconnection of two hypercubes

The bicube: an interconnection of two hypercubes

Survey on path and cycle embedding in some networks

Fault-tolerant panconnectivity of augmented cubes

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