Consider the graph given above. Add an edge so the resulting graph has an Euler circuit (without repeating an existing edge).
Now give an Euler circuit through the graph with this new edge by listing the vertices in the order visited.
lrc.alasu.edu/webwork2_course_files/MAT256/tmp/gif/cjones-3979-setset10prob1image1.png
Sorry, cannot access webwork sites unless registered.
You can use "snip" to copy the screen and post the copy at a photo sharing site such as imageshack.
To add an edge so that the resulting graph has an Euler circuit, we need to identify two vertices with odd degrees and connect them.
Looking at the given graph, we can see that vertices "D" and "F" have odd degrees (degree 3 for both). To create an Euler circuit, we will add an edge between "D" and "F".
Now, the new graph with the added edge will have the following vertices and edges:
Vertices: A, B, C, D, E, F
Edges: AB, BC, CD, AD, AE, AF, DE, DF
To provide an Euler circuit through this graph with the new edge, we need to list the vertices in the order visited. Starting from any vertex, we need to traverse each edge exactly once and return to the starting vertex.
One possible Euler circuit for this graph can be:
A -> B -> C -> D -> F -> A -> E -> D -> C -> B -> A -> F -> E -> A
Please note that there can be other valid Euler circuits for this graph as well.
To add an edge to a graph and form an Euler circuit, you need to find two vertices with odd degrees and connect them with a new edge. An Euler circuit can only exist in a graph if all vertices have an even degree, except for exactly two vertices, which have an odd degree.
However, you have not provided the graph or the image to which you are referring. Kindly provide the graph or the image so that I can explain how to add an edge and find an Euler circuit.