Question

while edge ce is included in the graph, the graph is dropdown if edge ce were removed, the graph would be dropdown. the options for the dropdown are connected and disconnected. there is also a diagram on the right with points a, b, c, d, e, f and edges as shown.

Explanation:

Step1: Understand the concept of connected graph

A connected graph is a graph in which there is a path between every pair of vertices.

Step2: Analyze the graph with edge CE

When edge CE is included, we can check paths:

• From A: \(A - C - E - F\), \(A - C - B\), \(C - E - D\) etc. We can reach all vertices (A, B, C, D, E, F) from any starting vertex. So the graph is connected.

Step3: Analyze the graph without edge CE

If we remove edge CE:

• The sub - graph with vertices A, B, C has no path to vertices D, E, F (and vice - versa). So the graph is disconnected.

Answer:

While edge CE is included in the graph, the graph is connected. If edge CE were removed, the graph would be disconnected.