OCR Further Discrete AS 2019 June — Question 2

Exam BoardOCR
ModuleFurther Discrete AS (Further Discrete AS)
Year2019
SessionJune
TopicGroups

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}
  1. List the vertex degrees for each graph.
  2. Prove that the graphs are non-isomorphic. The two graphs are joined together by adding an arc connecting J and T .
    1. Explain how you know that the resulting graph is not Eulerian.
    2. 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 \(K _ { 7 }\).
  3. Explain why 12 arcs are needed connecting \(K _ { 3 }\) to \(K _ { 4 }\).