Electric Circui...

The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is

The reduced incidence matrix of a graph is given below

\(A = \left[ {\begin{array}{*{20}{c}} { - 1}&0&1&1&{ - 1}&0\\ 1&{ - 1}&0&0&0&{ - 1}\\ 0&1&{ - 1}&{ - 1}&1&0 \end{array}} \right]\)

The number of possible trees is

The graph associated with an electrical network has 8 branches and 5 nodes. The rank of the cut-set matrix and tie-set matrix respectively can be no more than,