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A mesh network is a local area network topology in which the infrastructure nodes (i.e. bridges, switches, and other infrastructure devices) connect directly, dynamically and non-hierarchically to as many other nodes as possible and cooperate with one another to efficiently route data to and from clients.
A fully connected network, complete topology, or full mesh topology is a network topology in which there is a direct link between all pairs of nodes. In a fully connected network with n nodes, there are () direct links. Networks designed with this topology are usually very expensive to set up, but provide a high degree of reliability due to the ...
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
A torus interconnect is a switch-less topology that can be seen as a mesh interconnect with nodes arranged in a rectilinear array of N = 2, 3, or more dimensions, with processors connected to their nearest neighbors, and corresponding processors on opposite edges of the array connected. In this lattice, each node has 2N connections.
Its topology is captured by the graph of the connections between faces. A given mesh may actually contain multiple unconnected shells (or bodies); each body may be partitioned into multiple connected components each defined by their edge loop boundary. To represent a hollow object, the inside and outside surfaces are separate shells.
A hypercube is basically a multidimensional mesh network with two nodes in each dimension. Due to similarity, such topologies are usually grouped into a k-ary d-dimensional mesh topology family, where d represents the number of dimensions and k represents the number of nodes in each dimension. [1] Different hypercubes for varying number of nodes
The genus of a knot K is defined as the minimal genus of all Seifert surfaces for K. [4] A Seifert surface of a knot is however a manifold with boundary, the boundary being the knot, i.e. homeomorphic to the unit circle.