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The maximum degree of any vertex in a simple graph with n vertices is
- a)n
- b)n- 1
- c)n + 1
- d)2n -1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The maximum degree of any vertex in a simple graph with n vertices isa...
The maximum degree of any vertex in simple graph is:
total edges
since number of edges are 'n'
so degree will be
total edges
since number of edges are 'n'so degree will be
Most Upvoted Answer
The maximum degree of any vertex in a simple graph with n vertices isa...
The maximum degree of any vertex in a simple graph with n vertices is n-1.
Explanation:
- In a simple graph, each edge connects two distinct vertices and there are no loops or multiple edges.
- The degree of a vertex is the number of edges incident to it, i.e., the number of edges connected to that vertex.
- In a simple graph with n vertices, the maximum degree of any vertex can be n-1.
- This is because a vertex can be connected to all other vertices in the graph except itself, which gives a maximum of n-1 edges incident to it.
- If a vertex has degree n or more, then it means that it is connected to all other vertices in the graph, which would make the graph a complete graph.
- A complete graph with n vertices has n(n-1)/2 edges, which is greater than the maximum number of edges possible in a simple graph with n vertices (which is n-1 choose 2 = (n-1)(n-2)/2).
- Therefore, the maximum degree of any vertex in a simple graph with n vertices is n-1.
Explanation:
- In a simple graph, each edge connects two distinct vertices and there are no loops or multiple edges.
- The degree of a vertex is the number of edges incident to it, i.e., the number of edges connected to that vertex.
- In a simple graph with n vertices, the maximum degree of any vertex can be n-1.
- This is because a vertex can be connected to all other vertices in the graph except itself, which gives a maximum of n-1 edges incident to it.
- If a vertex has degree n or more, then it means that it is connected to all other vertices in the graph, which would make the graph a complete graph.
- A complete graph with n vertices has n(n-1)/2 edges, which is greater than the maximum number of edges possible in a simple graph with n vertices (which is n-1 choose 2 = (n-1)(n-2)/2).
- Therefore, the maximum degree of any vertex in a simple graph with n vertices is n-1.
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