Eulerian & semi-Eulerian Graphs (Edexcel A-Level Further Mathematics): Flashcards

Path visiting every edge exactly once

Circuit, every edge once, starts & ends at same vertex

Number of edges connected to it

All vertices even order & graph connected

Exactly 2 vertices odd order & graph connected

Disconnected OR more than 2 odd vertices

Starts at one odd vertex, ends at other odd vertex

Contributes 2 to the vertex's order

Graph must be connected

Semi-Eulerian (if connected)