1. STARTER: CAN YOU FIND A WAY OF CROSSING ALL THE BRIDGES EXACTLY ONCE? Here’s what this question would look like drawn as a graph

2. EULER & THE SEVEN BRIDGES OF KÖNIGSBERG Euler’s challenge was to create a walk through the city that would cross each bridge once and only once. This problem is considered to be the 1 st in history that deals with graph theory and helped developed the branch of maths known as topology. He eventually proved, mathematically, that it is impossible because of the degree of each vertex. Wikipedia

3. EULERIAN TRAILS AS Maths Decision 1

4. ARE YOU ABLE TO DRAW THE FIGURE WITHOUT LIFTING YOUR PEN AND WITHOUT GOING OVER THE SAME EDGE TWICE?

11. START LOOKING FOR PATTERNS… CAN YOU DRAW ANY CONCLUSIONS?

12. An Eulerian graph is a connected graph which has a closed trail containing every arc precisely once

13. A semi-Eulerian graph is a connected graph which has a trail containing every arc precisely once

14. Some graphs are neither Eulerian nor semi-Eulerian.

15. CAN YOU SORT THEM AS EULERIAN, SEMI- EULERIAN, AND NON-EULERIAN?

16. Non-EulerianSemi-EulerianEulerian