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The set of current loop equations associated with the tie sets of the original graph and tree is identical to the set of voltage node-pair equations associated with the cut sets of the dual graph. [40] The following table lists dual concepts in topology related to circuit theory. [41] Figure 2.5. The dual graph of the graph in figure 2.2.
The circuit rank controls the number of ears in an ear decomposition of a graph, a partition of the edges of the graph into paths and cycles that is useful in many graph algorithms. In particular, a graph is 2-vertex-connected if and only if it has an open ear decomposition. This is a sequence of subgraphs, where the first subgraph is a simple ...
Indeed, a graph has treewidth at most 2 if and only if it has branchwidth at most 2, if and only if every biconnected component is a series–parallel graph. [4] [5] The maximal series–parallel graphs, graphs to which no additional edges can be added without destroying their series–parallel structure, are exactly the 2-trees.
Circuit topology splits any entangled chains (including prime knots) into basic structural units called soft contacts, and lists simple rules on how soft contacts can be put together. [3] [4] An advantage of circuit topology is that it can be applied to open linear chains with intra-chain interactions, so-called hard contacts. [5]
Multiple feedback topology circuit. Multiple feedback topology is an electronic filter topology which is used to implement an electronic filter by adding two poles to the transfer function. A diagram of the circuit topology for a second order low pass filter is shown in the figure on the right.
In mathematics, topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. [1] It also studies immersions of graphs. Embedding a graph in a surface means that we want to draw the graph on a surface, a sphere for example, without two edges ...
The Detroit Lions have taken away a fan's season tickets after he was involved in a verbal altercation with Green Bay Packers coach Matt LaFleur.
Generalization of circuit theory based on scalar quantities to vectorial currents is a necessity for newly evolving circuits such as spin circuits. [clarification needed] Generalized circuit variables consist of four components: scalar current and vector spin current in x, y, and z directions. The voltages and currents each become vector ...