The adjoining graph
Show Hint
- connected
- disconnected
- Neither connected nor disconnected
- None of the above
The Correct Option is A
Solution and Explanation
To determine whether the graph is connected or disconnected, we need to understand these concepts:
- Connected Graph: A graph is connected if there is a path between every pair of vertices.
- Disconnected Graph: A graph is disconnected if at least one pair of vertices does not have a path between them.
Now, let's analyze the given graph:
The graph consists of two main components:
- A cycle on the left (square shape) and another connected structure on the right (diamond shape).
- The square is connected to the diamond through a vertex, ensuring all parts are reachable.
Hence, there is a path between every pair of vertices in the graph, making it a connected graph.
Conclusion: The graph is connected.
Top Questions on Graph Theory
- The coefficient of \( x^{50} \) in \( (1 + x)^{101} (1 - x + x^2)^{100} \) is:
- VITEEE - 2024
- Mathematics
- Graph Theory
Suppose a minimum spanning tree is to be generated for a graph whose edge weights are given below. Identify the graph which represents a valid minimum spanning tree?
\[\begin{array}{|c|c|}\hline \text{Edges through Vertex points} & \text{Weight of the corresponding Edge} \\ \hline (1,2) & 11 \\ \hline (3,6) & 14 \\ \hline (4,6) & 21 \\ \hline (2,6) & 24 \\ \hline (1,4) & 31 \\ \hline (3,5) & 36 \\ \hline \end{array}\]
Choose the correct answer from the options given below:
- CUET (PG) - 2025
- Data Science
- Graph Theory
Match LIST-I with LIST-II
Choose the correct answer from the options given below:
- CUET (PG) - 2025
- Data Science
- 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 \( G \)?- Want to practice more? Try solving extra ecology questions todayView All Questions