Branch of a tree, cotree

A branch of a tree is called twig. If there are n number of nodes on a graph then the tree of a graph contains ( n-1)  twigs. Cotree A set of branches forming a complement of tree is called cotree. The number of branches of a cotree equals b-(n-1) where b is number of branches of a grap...

Subgraph, path, rank of a graph, tree.

A subgraph is a subset of branches and nodes of a graph. There are two types of a subgraph. If the subgraph contains branches and nodes less in number than those on the graph, then a subgraph is called proper subgraph. If a subgraph contains all the nodes of a graph and the branches, then a subgraph is called improper subgraph. A path is a improper subgraph such that, i) At the terminating node only one branch is incident. ii) At the remaining nodes, two branches are incident. If a path exists between  any pair of nodes, then graph is called...

Colpitts oscillator..

The colpitts oscillator is similar to the op-amp phase shift oscillator, except that an LC network is used to produce the necessary phase shift in the feedback voltage. In this case the LC network acts as a filter that passes the oscillating frequenc...