incidance matrix, tie set matrix, cut set matrix

CUT SET MATRIX

A cut set matrix in graph theory, we generally talk of fundamental cut-set matrix. A cut-set is a minimum set of branches of a connected graph such that when removed these branches from the graph, then the graph gets separated into 2 distinct parts called sub-graphs and the cut set matrix is the matrix which is obtained by row-wise taking one cut-set at a time. The cutset matrix is denoted by symbol [Qf].

wo sub-graphs are obtained from a graph by selecting cut-sets consisting of branches [1, 2, 5, 6].

Thus, in other words we can say that fundamental cut set of a given graph with reference to a tree is a cut-set formed with one twig and remaining links. Twigs are the branches of tree and links are the branches of co-tree.

Thus, the number of cutset is equal to the number of twigs.

[Number of twigs = N – 1]

Where, N is the number of nodes of the given graph or drawn tree.

The orientation of cut-set is the same as that of twig and that is taken positive.

Steps to Draw Cut Set Matrix

There are some steps one should follow while drawing the cut-set matrix. The steps are as follows-

Draw the graph of given network or circuit (if given).

Then draw its tree. The branches of the tree will be twig.

Then draw the remaining branches of the graph by dotted line. These branches will be links.

Each branch or twig of tree will form an independent cut-set.

Write the matrix with rows as cut-set and column as branches.

Orientation in Cut Set Matrix

Qij = 1; if branch J is in cut-set with orientation same as that of tree branch.

Qij = -1; if branch J is in cut-set with orientation opposite to that of branch of tree.

Qij = 0; if branch J is not in cut-set.

Example 1