Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Optimal communication primitives on the generalized hypercube network
Journal of Parallel and Distributed Computing
Highly fault-tolerant routings and fault-induced diameter for generalized hypercube graphs
Journal of Parallel and Distributed Computing
Ring, torus and hypercube architectures/algorithms for parallel computing
Parallel Computing - Special Anniversary issue
Pancyclicity of recursive circulant graphs
Information Processing Letters
Efficient Resource Placement in Hypercubes Using Multiple-Adjacency Codes
IEEE Transactions on Computers
Uniform Approach for Solving some Classical Problems on a Linear Array
IEEE Transactions on Parallel and Distributed Systems
On Balancing Sorting on a Linear Array
IEEE Transactions on Parallel and Distributed Systems
Hamiltonian properties on the class of hypercube-like networks
Information Processing Letters - Devoted to the rapid publication of short contributions to information processing
Vertex-pancyclicity of edge-face-total graphs
Discrete Applied Mathematics
Task assignment in heterogeneous computing systems
Journal of Parallel and Distributed Computing
Geodesic pancyclicity and balanced pancyclicity of Augmented cubes
Information Processing Letters
Node-pancyclicity and edge-pancyclicity of hypercube variants
Information Processing Letters
Discrete Applied Mathematics
The m-pancycle-connectivity of a WK-Recursive network
Information Sciences: an International Journal
The pancyclicity and the Hamiltonian-connectivity of the generalized base-b hypercube
Computers and Electrical Engineering
The panconnectivity and the pancycle-connectivity of the generalized base-b hypercube
The Journal of Supercomputing
Edge-pancyclicity of Möbius cubes
Information Processing Letters
Complete path embeddings in crossed cubes
Information Sciences: an International Journal
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Recently, Chan et al. introduced geodesic-pancyclic graphs [H.C. Chan, J.M. Chang, Y.L. Wang, S.J. Horng, Geodesic-pancyclic graphs, Discrete Applied Mathematics 155 (15) (2007) 1971-1978] and weakly geodesic pancyclicity [H.C. Chan, J.M. Chang, Y.L. Wang, S.J. Horng, Geodesic-pancyclicity and fault-tolerant panconnectivity of augmented cubes, Applied Mathematics and Computation 207 (2009) 333-339]. Hsu et al. proposed a new cycle-embedding property called balanced pancyclicity [H.C. Hsu, P.L. Lai, C.H. Tsai, Geodesic pancyclicity and balanced pancyclicity of augmented cubes, Information Processing Letters 101 (2007) 227-232]. For a graph G(V,E) and any two vertices x and y of V, a cycle R containing x and y can be divided into two paths, Pt"1 and Pt"2, joining x and y such that len(Pt"1)@?len(Pt"2), where len(@l) denotes the length of the path @l. A geodesic cycle contains Pt"1, which is the shortest path joining x and y in G, whereas, in a balanced cycle of an even (respectively, odd) length, len(Pt"1)=len(Pt"2) (respectively, len(Pt"1)=len(Pt"2)-1). A graph is weakly geodesic pancyclic (respectively, balanced pancyclic) if every two vertices x and y are contained in a geodesic cycle (respectively, balanced cycle) from Max(3,2Dist(x,y)) to N, where N is the order of the graph. The interconnection network considered in this paper is the generalized base-b hypercube, which is an attractive variant of the well-known hypercube. In fact, the generalized base-b hypercube is the Cartesian product of complete graphs with b vertices. The generalized base-b hypercube is superior to the hypercube in many criteria, such as diameter, connectivity, and fault diameter. In this paper, we study weakly geodesic pancyclicity and balanced pancyclicity of the generalized base-b hypercube. We show that the generalized base-b hypercube is weakly geodesic pancyclic for b=3 and balanced pancyclic for b=4.