Eulerian Trails and Circuits (Extension) (VCE SSCE General Mathematics): Flashcards

Path through graph travelling each edge exactly once

Eulerian trail that starts and ends at same vertex

Connected graph with 0 or 2 odd-degree vertices

Connected graph where all vertices have even degree

Number of edges connected to that vertex

Must start at one odd vertex, end at the other

Both Eulerian trail and circuit

Only Eulerian trail (no circuit)

Neither Eulerian trail nor circuit

Minimises time and distance by not repeating paths