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Which of the following properties of the circuits of a graph are correct?

1. The minimum number of branches possible in a circuit will be equal to the number of elements in a circuit.

2. There are exactly two paths between any pair of vertices in a circuit.

3. There are at least two branches in a circuit.

Select the correct answer using the code given below.

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UPSC ESE Electronics & Communication 2022 Official Paper
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  1. 1 and 2 only
  2. 1 and 3 only
  3. 2 and 3 only
  4. 1, 2 and 3

Answer (Detailed Solution Below)

Option 2 : 1 and 3 only
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Detailed Solution

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The number of nodes present in a graph will be equal to the number of principal nodes present in an electric circuit.

The number of branches present in a graph will be less than or equal to the number of branches present in an electric circuit.

In a graph there is one and only one path between every pair of vertices.

Branches are the connections between nodes. A branch is an element(resistor, capacitor, source).

The number of branches in a circuit is equal to the number of elements.

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