Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Interconnection Networks and Their Eigenvalues
ISPAN '02 Proceedings of the 2002 International Symposium on Parallel Architectures, Algorithms and Networks
On the ith graphs of the Johnson scheme
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
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Graphs are used in modeling interconnections networks and measuring their properties. Knowing and understanding the graph theoretical/combinatorial properties of the underlying networks are necessary in developing more efficient parallel algorithms as well as fault-tolerant communication/routing algorithms [1]. The hypercube is one of the most versatile and efficient networks yet discovered for parallel computation. One generalization of the hypercube is the n-cube Q(n,m) which is a graph whose vertices are all the binary n- tuples, such that two vertices are adjacent whenever they differ in exactly m coordinates. The k-subgraph of the Generalized n-cube Qk(n,m) is the induced subgraph of the n-cube Q(n,m) where q=2, such that a vertex v ∈ V(Qk(n,m)) if and only if v ∈ V(Q(n,m)) and v is of parity k. This paper presents some degree properties of Qk(n,m) as well as some isomorphisms it has with other graphs, namely: 1) Qn-1 (n,2) is isomorphic to Kn 2) Qk(n,2i) is isomorphic to Gi(n,k) 3) QS(n,2i) is isomorphic to SGi(n).