Graph Theory

Walk

a sequence of vertices in a graph, where each pair of consecutive vertices is connected by an edge

Trail

a walk through a graph where no edge is repeated

Circuit

a path that starts and ends at the same vertex

Path

a sequence of edges connecting a series of distinct vertices in a graph

Cycle

a path within a graph that starts and ends at the same vertex, where no vertices are repeated along the path, essentially creating a closed loop within the graph

Euler Trail

a trail in a finite graph that visits every edge exactly once

Euler Circuit

a circuit that traverses every edge of a graph exactly once, starting and ending at the same vertex

Hamilton Path

a path in a graph that visits every vertex exactly once

Hamilton Cycle

a closed path in a graph that visits each vertex exactly once and ends at the same vertex it started at