Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Folded Petersen Cube Networks: New Competitors for the Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Mesh-Connected Trees: A Bridge Between Grids and Meshes of Trees
IEEE Transactions on Parallel and Distributed Systems
Products of Networks with Logarithmic Diameter and Fixed Degree
IEEE Transactions on Parallel and Distributed Systems
Generalized Hypercube and Hyperbus Structures for a Computer Network
IEEE Transactions on Computers
Note: Cancellation properties of products of graphs
Discrete Applied Mathematics
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In this paper, we study containment properties of graphs in relation with the Cartesian product operation. These results can be used to derive embedding results for interconnection networks for parallel architectures. First, we show that the isomorphism of two Cartesian powers G^r and H^r implies the isomorphism of G and H, while G^r@?H^r does not imply G@?H, even for the special cases when G and H are prime, and when they are connected and have the same number of nodes at the same time. Then, we find a simple sufficient condition under which the containment of products implies the containment of the factors: if @?"i"="1^nG"i@?@?"j"="1^nH"j, where all graphs G"i are connected and no graph H"j has 4-cycles, then each G"i is a subgraph of a different graph H"j. Hence, if G is connected and H has no 4-cycles, then G^r@?H^r implies G@?H. Finally, we focus on the particular case of products of graphs with the linear array. We show that the fact that GxL"n@?HxL"n does not imply that G@?H even in the case when G and H are connected and have the same number of nodes. However, we find a sufficient condition under which GxL"n@?HxL"n implies G@?H.