MYP Extended Mathematics Paths and Cycles Key Definitions

The problem of finding a shortest closed route that traverses every edge of a weighted graph at least once.

A graph where every pair of distinct vertices is joined by an edge.

A path that starts and ends at the same vertex and does not pass through any vertex more than once.

The **degree** of a vertex is the number of edges meeting at that vertex (counting multiple edges separately).

A trail that uses every edge exactly once and ends at the starting vertex.

A trail that uses every edge exactly once but starts and ends at different vertices.

A Hamiltonian path that returns to its starting vertex.

A path that visits every vertex exactly once.

A walk through a graph that does not repeat any edge.