Test: Graph Theory - Electrical Engineering (EE) MCQ

The circuit 1 and 2 are redrawn as below. 3 and 4 can not be redrawn on a plane without crossing other branch.

Other three circuits can be drawn on plane without crossing

l = b - ( n - 1) = 4.

There are 4 node and 6 branches.
t = n - 1 = 3, l = b - n + 1 = 3

From fig. it can be seen that afhg is a tree of given graph

Number of branch = 8
Number of link = 4
Number of twigs = 8 - 4 = 4
Number of twigs =number of independent node equation.

The number of independent node equation are n - 1.

 Number of branch b=8
Number of link l = 4
Number of twigs t = b - l = 4
rank of matrix = n - 1 = t = 4

We know the branch current and loop current are related as

f-loop 1 include branch (2, 4, 6, 7) and direction of branch–2 is opposite to other (B only).

Concept:

Tree: A tree is a subgraph of the main graph which connects all the nodes without forming a closed loop.

Connected Graph:

1) If there exists at least one branch between any of the two nodes of a graph, then it is called as a connected graph.

2) That means each node in the connected graph will be having one or more branches that are connected to it. So, no node will present as isolated or separated.

Complete Graph:

A complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.

The number of trees of a graph can be calculated by using the following formula:

Number of trees = n^n-2, n > 2 for completely connected graph

= |[A_r] [A_r]^T | for just connected graph

A_r is reduced incidence matrix. 

Analysis:

The given graph is a completely connected graph

Number of trees = n^n-2

Where n = 4

Number of trees = 4^(4-2) = 4² = 16