Which of the following statements is true?
Show Hint
- Some trees are graphs
- All graphs are trees
- All trees are graphs
- No tree is a graph
The Correct Option is C
Solution and Explanation
Therefore, all trees are graphs, but not all graphs are trees because graphs can have cycles and may not be connected.
Thus, the correct answer is \( \text{All trees are graphs} \).
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?
Match the following:
The union and intersection of the graphs G and H are respectively
The cut vertex set of the graph is
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