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The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is
- a)11
- b)12
- c)13
- d)14
Correct answer is option 'B'. Can you explain this answer?
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The graph of a network has 8 nodes and 5 independent loops. The number...
The number of branches in a network graph
To find the number of branches in a network graph, we need to understand the components of a network graph and how they are connected.
Components of a network graph
1. Nodes: Nodes represent the points or vertices in the network graph. In this case, there are 8 nodes.
2. Loops: Loops are closed paths in the network graph where we can travel through different branches and return to the starting point without visiting any node twice. In this case, there are 5 independent loops.
3. Branches: Branches are the individual connections or edges between nodes in the network graph.
Determining the number of branches
The number of branches in a network graph can be determined using the formula:
Number of branches = Number of nodes - Number of loops + 1
Applying this formula to the given problem:
Number of nodes = 8
Number of loops = 5
Number of branches = 8 - 5 + 1
= 4 + 1
= 5
Therefore, the number of branches in the graph is 5.
Identifying the correct answer
Now let's evaluate the options given:
a) 11 branches
b) 12 branches (Correct Answer)
c) 13 branches
d) 14 branches
Since the calculated number of branches is 5, option b) with 12 branches matches the calculated value. Therefore, the correct answer is option b) - 12 branches.
To find the number of branches in a network graph, we need to understand the components of a network graph and how they are connected.
Components of a network graph
1. Nodes: Nodes represent the points or vertices in the network graph. In this case, there are 8 nodes.
2. Loops: Loops are closed paths in the network graph where we can travel through different branches and return to the starting point without visiting any node twice. In this case, there are 5 independent loops.
3. Branches: Branches are the individual connections or edges between nodes in the network graph.
Determining the number of branches
The number of branches in a network graph can be determined using the formula:
Number of branches = Number of nodes - Number of loops + 1
Applying this formula to the given problem:
Number of nodes = 8
Number of loops = 5
Number of branches = 8 - 5 + 1
= 4 + 1
= 5
Therefore, the number of branches in the graph is 5.
Identifying the correct answer
Now let's evaluate the options given:
a) 11 branches
b) 12 branches (Correct Answer)
c) 13 branches
d) 14 branches
Since the calculated number of branches is 5, option b) with 12 branches matches the calculated value. Therefore, the correct answer is option b) - 12 branches.
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The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph isa)11b)12c)13d)14Correct answer is option 'B'. Can you explain this answer?
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The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph isa)11b)12c)13d)14Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph isa)11b)12c)13d)14Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph isa)11b)12c)13d)14Correct answer is option 'B'. Can you explain this answer?.
The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph isa)11b)12c)13d)14Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph isa)11b)12c)13d)14Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph isa)11b)12c)13d)14Correct answer is option 'B'. Can you explain this answer?.
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