Test: Graph Theory
10 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | Test: Graph Theory
Consider the following circuits :
The planner circuits are
The circuit 1 and 2 are redrawn as below. 3 and 4 can not be redrawn on a plane without crossing other branch.
Consider the following graphs
Non-planner graphs are
Other three circuits can be drawn on plane without crossing
A graph of an electrical network has 4 nodes and 7 branches. The number of links l, with respect to the chosen tree, would be
l = b - (n - 1) = 4.
For the graph shown in fig.correct set is
There are 4 node and 6 branches.
t = n - 1 = 3, l = b - n + 1 = 3
A tree of the graph shown in fig. is
From fig. it can be seen that a f h g is a tree of given graph
Branch current and loop current relation are expressed in matrix form as
where ij represent branch current and Ik loop current. The number of independent node equation are
Number of branch = 8
Number of link = 4
Number of twigs = 8 - 4 = 4
Number of twigs = number of independent node equation.
If the number of branch in a network is b, thenumber of nodes is n and the number of dependent loop is l, then the number of independent node equations will be
The number of independent node equation are n - 1.
Branch current and loop current relation are expressed in matrix form as
.
where ij represent branch current and Ik loop current.
The rank of incidence matrix is
Number of branch b = 8
Number of link l = 4
Number of twigs t = b - l = 4
rank of matrix = n - 1 = t = 4
A network has 8 nodes and 5 independent loops. The number of branches in the network is
Independent loops = link
l = b - (n - 1)
= 5 = b - 7
b = 12
A branch has 6 node and 9 branch. The independent loops are
Independent loop = link
l = b - (n-1) = 4
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