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Which of the following statements is/are TRUE for undirected graphs?
P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even.
P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even.
- a)P only
- b)Q only
- c)Both P and Q
- d)Neither P nor Q
Correct answer is option 'C'. Can you explain this answer?
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Which of the following statements is/are TRUE for undirected graphs?P:...
Q: Sum of degrees of all vertices = 2×(number of edges)
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Which of the following statements is/are TRUE for undirected graphs?P:...
Number of odd degree vertices is even (P):
- In an undirected graph, the degree of a vertex is the number of edges incident to that vertex.
- If the graph has an even number of edges incident to each vertex, then the sum of the degrees of all vertices will be even.
- If a graph has an odd degree vertex, it must be paired with another odd degree vertex to maintain the even sum of degrees.
- Therefore, in undirected graphs, the number of odd degree vertices is always even.
Sum of degrees of all vertices is even (Q):
- The sum of the degrees of all vertices in an undirected graph is always even.
- This is because each edge contributes 2 to the sum of degrees (1 for each incident vertex).
- Since the total number of edges is always even (each edge is counted twice), the sum of degrees will also be even.
Therefore, both statements P and Q are true for undirected graphs. The number of odd degree vertices is even, and the sum of degrees of all vertices is even.
- In an undirected graph, the degree of a vertex is the number of edges incident to that vertex.
- If the graph has an even number of edges incident to each vertex, then the sum of the degrees of all vertices will be even.
- If a graph has an odd degree vertex, it must be paired with another odd degree vertex to maintain the even sum of degrees.
- Therefore, in undirected graphs, the number of odd degree vertices is always even.
Sum of degrees of all vertices is even (Q):
- The sum of the degrees of all vertices in an undirected graph is always even.
- This is because each edge contributes 2 to the sum of degrees (1 for each incident vertex).
- Since the total number of edges is always even (each edge is counted twice), the sum of degrees will also be even.
Therefore, both statements P and Q are true for undirected graphs. The number of odd degree vertices is even, and the sum of degrees of all vertices is even.
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Which of the following statements is/are TRUE for undirected graphs?P: Number of odd degree vertices is even.Q: Sum of degrees of all vertices is even.a)P onlyb)Q onlyc)Both P and Qd)Neither P nor QCorrect answer is option 'C'. Can you explain this answer?
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