Which of the following statements is not true?
Show Hint
- 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
The Correct Option is D
Solution and Explanation
- 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 \( 4 \).
Top Questions on Graph Theory
Let \( G \) be a simple, unweighted, and undirected graph. A subset of the vertices and edges of \( G \) are shown below.
It is given that \( a - b - c - d \) is a shortest path between \( a \) and \( d \); \( e - f - g - h \) is a shortest path between \( e \) and \( h \); \( a - f - c - h \) is a shortest path between \( a \) and \( h \). Which of the following is/are NOT the edges of \( G \)?- Consider the given graph and shortest paths: The shortest paths given are: \[ a - b - c - d, \quad e - f - g - h, \quad a - f - c - h \] Which of the following cannot be an edge in the original graph?
The union and intersection of the graphs G and H are respectively
Match the following:
The cut vertex set of the graph is
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