Language and properties of graphsAQA A-Level Further Maths: Mind map

Exam questions on Language and properties of graphs

1. A graph $G$ has vertices $A,\ B,\ C,\ D,\ E$ and seven edges: $AB$, $AC$, $BC$, $BD$, $CD$, $CE$ and $DE$.
   Write down a trail in $G$ that uses every edge exactly once.2 marks
2. A graph $H$ has vertices $P,\ Q,\ R,\ S,\ T,\ U$ and eight edges: $PQ$, $QR$, $RS$, $ST$, $TU$, $UP$, $PS$ and $QT$.
   Explain why $H$ is neither Eulerian nor semi-Eulerian.2 marks
3. A connected simple graph $K$ has six vertices. Five of the vertices have degrees $2,\ 2,\ 3,\ 3$ and $4$, and the sixth vertex has degree $x$.
   Show that $x$ is even, and state with a reason whether $K$ is Eulerian, semi-Eulerian or neither.3 marks