516 research outputs found
The edge fault-diameter of Cartesian graph bundles
AbstractA Cartesian graph bundle is a generalization of a graph covering and a Cartesian graph product. Let G be a kG-edge connected graph and D̄c(G) be the largest diameter of subgraphs of G obtained by deleting c<kG edges. We prove that D̄a+b+1(G)≤D̄a(F)+D̄b(B)+1 if G is a graph bundle with fibre F over base B, a<kF, and b<kB. As an auxiliary result we prove that the edge-connectivity of graph bundle G is at least kF+kB
ON VULNERABILITY MEASURES OF NETWORKS
As links and nodes of interconnection networks are exposed to failures, one of the most important features of a practical networks design is fault tolerance. Vulnerability measures of communication
networks are discussed including the connectivities, fault diameters, and measures based on Hosoya-Wiener polynomial. An upper bound for the edge fault diameter of product graphs is proved
ON VULNERABILITY MEASURES OF NETWORKS
As links and nodes of interconnection networks are exposed to failures, one of the most important features of a practical networks design is fault tolerance. Vulnerability measures of communication
networks are discussed including the connectivities, fault diameters, and measures based on Hosoya-Wiener polynomial. An upper bound for the edge fault diameter of product graphs is proved
On connectedness and hamiltonicity of direct graph bundles
A necessary and sufficient condition for connectedness of direct graph bundles is given where the fibers are cycles.
We also prove that all connected direct graph bundles are Hamiltonian
PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks
In this paper, we present PolarStar, a novel family of diameter-3 network
topologies derived from the star product of two low-diameter factor graphs. The
proposed PolarStar construction gives the largest known diameter-3 network
topologies for almost all radixes. When compared to state-of-the-art diameter-3
networks, PolarStar achieves 31% geometric mean increase in scale over
Bundlefly, 91% over Dragonfly, and 690% over 3-D HyperX.
PolarStar has many other desirable properties including a modular layout,
large bisection, high resilience to link failures and a large number of
feasible sizes for every radix. Our evaluation shows that it exhibits
comparable or better performance than other diameter-3 networks under various
traffic patterns.Comment: 13 pages, 13 figures, 4 table
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