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 $X=C_stimes^{alpha}C_t$ 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