Graph Theory Definitons

Walk

A sequence of edges where verticies may repeat

Path

A walk where no vertex is repeated (except possibly start/end if it’s a cycle)

Trail

A walk where no edge is repeated

Cycle

A path that starts and ends at the same vertex

Hamiltonian Cycle

A cycle that visits every vertex exactly pnce before reurning to the start

Connected Graph

A graph where every pair of verticies is linked by a path

Loop

An edge that starts and ends at the same vertex

Simple graph

A graph where edges(arcs) have a direction shown by arrows

Vertex/Node

A point in a graph

Edge/Arc

A line joining two vertices. In directed graphs(called arcs) have direction

Subgraph

A graph formed from some of the vertices and edges of a larger path

Order/Valancey/ Degree of a Vertex

The number of edges incident to a vertex. A loop counts twice