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The number of twigs and links in a connected network graph with 'n' nodes and 'b' branches are, respectively.
  • a)
    n - 2, b - n - 2
  • b)
    n - 1, b - n + 1
  • c)
    n, 2n - b
  • d)
    2n, 2n - b
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The number of twigs and links in a connected network graph with n node...

Explanation:

Number of Twigs:
- The number of twigs in a connected network graph with n nodes can be calculated using the formula: n - 1.
- Each twig is a path in the graph that does not form a loop. Since a connected network graph has n nodes and n - 1 edges, the number of twigs will be n - 1.

Number of Links:
- The number of links in a connected network graph with n nodes and b branches can be calculated using the formula: b - n + 1.
- A branch is a path that forms a loop in the graph. Since the graph is connected, there will be b branches. Therefore, the number of links will be b - n + 1.

Therefore, the correct answer is option B: n - 1, b - n + 1.
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Community Answer
The number of twigs and links in a connected network graph with n node...
Concept:
Tree: A tree is a sub graph of main graph which connects all the nodes without forming a closed loop.
For a graph with ‘n’ nodes, the rank of tree = n – 1
Any tree for a given graph can be constructed with (n–1) branches.
Twig: The branch of a tree is called as twig indicated by thick Line. Any tree with n nodes has (n – 1) twigs.
Co-tree: The set of branches in a graph other than tree branches form a co tree.
Link: The branch of a co tree is called link indicated by dotted Line.
For any graph with n nodes and b branches, the numbers of links is given by:
= b – n + 1
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The number of twigs and links in a connected network graph with n nodes and b branches are, respectively.a)n - 2, b - n - 2b)n - 1, b - n + 1c)n, 2n - bd)2n, 2n - bCorrect answer is option 'B'. Can you explain this answer?
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