Identify the cut vertices in the below graph ?OptionsC and BC and AB and EB and A

To identify the cut vertices (or articulation points) in a graph, follow these steps:

1. Break Down the Problem

   • Define a cut vertex in graph theory: A cut vertex is a vertex which, when removed along with its edges, increases the number of connected components in the graph.
   • Analyze the graph in question to determine which vertices are cut vertices.

2. Relevant Concepts

   • Consider using a depth-first search (DFS) algorithm to find articulation points.
   • Use properties of DFS tree:
     • For a root node: it is a cut vertex if it has two or more children in the DFS tree.
     • For non-root nodes: it is a cut vertex if there exists a child such that no vertex in the child’s subtree has a back edge to one of the node’s ancestors.

3. Analysis and Detail

   • Without access to the graph, I cannot perform a concrete analysis.

   • However, label the vertices and explore their connectivity based on the given options:

     1. C
     2. BC
     3. AB
     4. EB
     5. A

   • Check the connections for each vertex based on the graph structure to see if removing that vertex disconnects parts of the graph.

4. Verify and Summarize

   • After checking the connection and applying the above criteria, verify which vertices, when removed, disconnect the graph.

Final Answer

From the provided options, determine the cut vertices based on the analysis of their connectivity. Since no specific graph is provided, I would recommend visiting the graph's structure to identify them correctly. If you can provide the graph or its connection details, I could offer more definitive assistance.