2 Two graphs are shown below.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8473d9aa-a4db-4001-ac71-e5fbbaee530c-2_396_353_1343_479}
\captionsetup{labelformat=empty}
\caption{Graph G1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8473d9aa-a4db-4001-ac71-e5fbbaee530c-2_399_328_1340_1233}
\captionsetup{labelformat=empty}
\caption{Graph G2}
\end{figure}
- List the vertex degrees for each graph.
- Prove that the graphs are non-isomorphic.
The two graphs are joined together by adding an arc connecting J and T .
- Explain how you know that the resulting graph is not Eulerian.
- Describe how the graph can be made Eulerian by adding one more arc.
The vertices of the graph \(K _ { 3 }\) are connected to the vertices of the graph \(K _ { 4 }\) to form the graph \(K _ { 7 }\).
- Explain why 12 arcs are needed connecting \(K _ { 3 }\) to \(K _ { 4 }\).