Question:
Which of the following statements is not true?
Which of the following statements is not true?
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For isomorphic graphs, the number of vertices and edges are always the same, but the graphs may have different layouts.
Updated On: May 3, 2025
- The number of vertices of any two isomorphic graphs is the same
- The number of edges of any two isomorphic graphs is the same
- The number of vertices and the number of edges of any two isomorphic graphs are the same
- The difference between the number of edges of any two isomorphic graphs must be one
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The Correct Option is D
Solution and Explanation
Isomorphic graphs are graphs that contain the same number of connections (edges) and vertices, but they may differ in appearance. For two graphs to be isomorphic:
- The number of vertices must be the same.
- The number of edges must be the same.
- The adjacency relationships between the vertices must be identical.
However, the statement "The difference between the number of edges of any two isomorphic graphs must be one" is false because isomorphic graphs will always have the same number of edges.
Therefore, the correct answer is \( 4 \).
- The number of vertices must be the same.
- The number of edges must be the same.
- The adjacency relationships between the vertices must be identical.
However, the statement "The difference between the number of edges of any two isomorphic graphs must be one" is false because isomorphic graphs will always have the same number of edges.
Therefore, the correct answer is \( 4 \).
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