Using Fleury's Algorithm in the graph to the bottom left, I deleted three edges and I got the graph to the bottom right. If I am currently at the starred vertex, list all possibilities for the edge I should travel next.
To determine the possibilities for the next edge to travel using Fleury's Algorithm, we need to analyze the given graph and its components.
First, let's understand Fleury's Algorithm:
1. Start at any vertex of the graph.
2. Select any adjacent edge that is not a bridge (i.e., not the only connection between two vertices).
3. Remove the selected edge from the graph.
4. Move to the other end of the selected edge and repeat steps 2 to 4 until no edges remain.
Now, let's apply this algorithm to the given graph:
Step 1: Start at the starred vertex (let's call it Vertex A).
Step 2: Check for adjacent edges that are not bridges. A bridge is an edge where its removal would increase the number of components (connected subgraphs) in the graph.
In the initial graph, based on the highlighted edges, we can see that there are three edges connected to Vertex A. Let's label them as Edge 1, Edge 2, and Edge 3.
* *
/ \ ===> / \
/ \ / \
/ \ / \
1 2 1 2
\ / \ /
\ / \ /
\ / \ /
3 3
Step 3: Remove one of the adjacent edges that is not a bridge. But before doing that, we need to identify which edges are not bridges by analyzing the resulting components.
Note: To determine if removing an edge creates a bridge, we delete the edge and check if the number of components increases. If it does, then the edge is a bridge.
After deleting three edges in our case, we only consider the remaining graph. It looks like this:
*
/ \
/ \
/ \
2
\ /
\ /
\ /
Here, we have only one component, meaning no bridge exists.
Now, let's look at the adjacent edges of Vertex A in the remaining graph. There is only one adjacent edge available: Edge 2.
Since it is not a bridge, we can choose Edge 2 as the next edge to traverse.
Finally, if you move along Edge 2, you will reach another vertex, and then you can repeat the steps to determine the next possible edge to travel.