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Panconnectivity and EdgePancyclicity of Faulty Recursive Circulant G(2 m, 4)
"... In this paper, we investigate a problem on embedding paths into recursive circulant G(2 m, 4) with faulty elements (vertices and/or edges) and show that each pair of vertices in recursive circulant G(2 m, 4), m ≥ 3, are joined by a faultfree path of every length from m + 1 to V (G(2 m, 4)\F)  − ..."
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In this paper, we investigate a problem on embedding paths into recursive circulant G(2 m, 4) with faulty elements (vertices and/or edges) and show that each pair of vertices in recursive circulant G(2 m, 4), m ≥ 3, are joined by a faultfree path of every length from m + 1 to V (G(2 m, 4)\F
PANCYCLICITY IN FAULTY KARY 2CUBES
"... We prove that a kary 2cube Qk2 with 3 faulty edges but where every vertex is incident with at least 2 healthy edges is bipancyclic, if k ≥ 3, and kpancyclic, if k ≥ 5 is odd (these results are optimal). ..."
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We prove that a kary 2cube Qk2 with 3 faulty edges but where every vertex is incident with at least 2 healthy edges is bipancyclic, if k ≥ 3, and kpancyclic, if k ≥ 5 is odd (these results are optimal).
Path and cycle embedding in faulty hypergraphs
"... The architecture of an interconnection network is usually represented by a graph. There exist mutually conflicting requirements in designing and topology of interconnection networks. It became almost impossible for us to design a network which is optimum in all aspects. The hypercube network is o ..."
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The architecture of an interconnection network is usually represented by a graph. There exist mutually conflicting requirements in designing and topology of interconnection networks. It became almost impossible for us to design a network which is optimum in all aspects. The hypercube network is one of the most popular topologies among the interconnection networks. It has widely used due to many of its attractive properties, including regular, symmetric, strong connectivity and relative small diameter [48, 64] etc. The first paper dealing directly with hamiltonian property and fault tolerant property appeared in 1976 Hayes [38]. Since that time the interest in hamiltonian property and faulttolerant property has been on increase. Many combinatorial, algebraic, and
Longest Cycles Embedding in Faulty Augmented Cube Networks
"... Abstract. The augmented cube nAQ is one of the most versatile and efficient interconnection networks (networks for short) so far discovered for parallel computation. In this paper, the topological structure of n dimensional augmented cube is analyzed. The properties related to cycle embedding in fau ..."
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in faulty nAQ have been investigated. Let F denote the set of fault links. This study demonstrates that when 32  − ≤ nF, for each nonfault link xy of augmented cube networks, xy lies on a longest fault free cycle which contains every nodes of nAQ. 1.
Pancyclicity and panconnectivity in augmented kary ncubes
"... Abstract—The augmented kary ncube AQn,k is a recently proposed interconnection network that incorporates an extension of a kary ncube Qkn inspired by the extension of a hypercube Qn to the augmented hypercube AQn (as developed by Choudom and Sunita). We extend a recent topological investigation ..."
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investigation of augmented kary ncubes by proving that any augmented kary ncube AQn,k is edgepancyclic and that AQ2,k is panconnected. Keywordsinterconnection networks; pancyclicity; panconnectivity; augmented kary ncube; I.
HypercubeLike Interconnection Networks with
, 2016
"... Panconnectivity and pancyclicity of hypercubelike interconnection networks with faulty elements. ..."
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Panconnectivity and pancyclicity of hypercubelike interconnection networks with faulty elements.
A New Property of Interconnection Networks
"... Abstract — A graph G is pancyclic if G includes cycles of all lengths and G is edgepancyclic if each edge lies on cycles of all lengths. A bipartite graph is edgebipancyclic if each edge lies on cycles of every even length from 4 to V (G). Two cycles with the same length m, C1 = ⟨u1, u2, · · ..."
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Abstract — A graph G is pancyclic if G includes cycles of all lengths and G is edgepancyclic if each edge lies on cycles of all lengths. A bipartite graph is edgebipancyclic if each edge lies on cycles of every even length from 4 to V (G). Two cycles with the same length m, C1 = ⟨u1, u2
Geodesic pancyclicity and balanced 5pancyclicity of 3ary ncube
 THE 25TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
"... Let G be a graph. For any two vertices x, y ∈ V (G), a cycle C is called (x, y)geodesic if there exists a shortest x − y path of G lies on C; and a cycle C is called (x, y)balanced if x, y ∈ V (C) and the distance of x and y in C is equal to ⌊V (C)/2 ⌋ (i.e.,dC(x, y) = max{dC(u, v)  u, v ∈ V ( ..."
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(C)}). A graph G is geodesic pancyclic if for any two vertices x, y ∈ V (G), there exists a (x, y)geodesic cycle of every length from max{2d(x, y), 3} to V (G). A graph G is balanced kpancyclic if for any two vertices x, y ∈ V (G), there exists a (x, y)balanced cycle of every length from max{2d
Two EdgeDisjoint Hamiltonian Cycles and TwoEqual Path Partition in Augmented Cubes
"... Abstract—The ndimensional hypercube network Qn is one of the most popular interconnection networks since it has simple structure and is easy to implement. The ndimensional augmented cube, denoted by AQn, an important variation of the hypercube, possesses several embedding properties that hypercube ..."
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(us, ut) and (vs, vt) of G, there exist two nodedisjoint paths P and Q satisfying that (1) P joins us and ut, and Q joins vs and vt, (2) P  = Q, and (3) every node of G appears in one path exactly once. In this paper, we first use a simple recursive method to construct two edge
Closure Concepts  a Survey
 Graphs and Combinatorics
"... In this paper we survey results of the following type (known as closure results). Let P be a graph property, and let C(u; v) be a condition on two nonadjacent vertices u and v of a graph G. Then G+uv has property P if and only if G has property P . The first and now wellknown result of this type ..."
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In this paper we survey results of the following type (known as closure results). Let P be a graph property, and let C(u; v) be a condition on two nonadjacent vertices u and v of a graph G. Then G+uv has property P if and only if G has property P . The first and now wellknown result
Results 1  10
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27