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The cut set consists of the tree branch which was not short-circuited and any of the links which are not short-circuited by the other tree branches. A cut set of a graph produces two disjoint subgraphs, that is, it cuts the graph into two parts, and is the minimum set of branches needed to do so. The set of network equations are formed by ...
This circuit is called the fundamental circuit of w.r.t. . It is analogous to the linear algebra fact, that if adding a vector x {\displaystyle x} to an independent vector set J {\displaystyle J} makes it dependent, then there is a unique linear combination of elements of J {\displaystyle J} that equals x {\displaystyle x} .
The dependent sets, the bases, or the circuits of a matroid characterize the matroid completely: a set is independent if and only if it is not dependent, if and only if it is a subset of a basis, and if and only if it does not contain a circuit. The collections of dependent sets, of bases, and of circuits each have simple properties that may be ...
Circuits over natural numbers are a mathematical model used in studying computational complexity theory.They are a special case of circuits.The object is a labeled directed acyclic graph the nodes of which evaluate to sets of natural numbers, the leaves are finite sets, and the gates are set operations or arithmetic operations.
A cut C = (S, T) is a partition of V of a graph G = (V, E) into two subsets S and T. The cut-set of a cut C = (S, T) is the set {(u, v) ∈ E | u ∈ S, v ∈ T} of edges that have one endpoint in S and the other endpoint in T. If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t ...
This set of cycles corresponds, in the dual graph of the given planar graph, to a set of cuts that form a Gomory–Hu tree of the dual graph, the minimum weight basis of its cut space. [21] Based on this duality, an implicit representation of the minimum weight cycle basis in a planar graph can be constructed in time O ( n log 3 n ...
The depth of a circuit is the maximum depth of any gate. Level is the set of all gates of depth . A levelled circuit is a circuit in which the edges to gates of depth comes only from gates of depth + or from the inputs. In other words, edges only exist between adjacent levels of the circuit.
In integrated circuit design, physical design is a step in the standard design cycle which follows after the circuit design.At this step, circuit representations of the components (devices and interconnects) of the design are converted into geometric representations of shapes which, when manufactured in the corresponding layers of materials, will ensure the required functioning of the components.