Graphs and Networks - Glossary

Front

What is a walk in graph theory?

Back

A sequence of vertices where each vertex is joined to the next by an edge, allowing for repeated vertices and edges.

Front

What is a trail in graph theory?

Back

A walk that has no repeated edges but can revisit vertices.

Front

What are adjacent vertices?

Back

Two vertices that are directly connected by at least one edge.

Front

What does it mean for a graph to be traversable?

Back

A network that can be drawn without lifting the pen from the page and without retracing any edge.

Front

What is a bipartite graph?

Back

A graph where vertices can be divided into two groups such that every edge connects a vertex from one group to a vertex from the other.

Front

What is an Eulerian trail?

Back

A trail that visits every edge of a graph exactly once.

Front

What is a Hamiltonian circuit?

Back

A circuit that visits every vertex of a graph exactly once and returns to the starting vertex.

Front

What is a complete graph?

Back

A graph in which every pair of distinct vertices is connected by a unique edge.

Front

What is a planar graph?

Back

A graph that can be drawn on a plane without any edges crossing.

Front

What is a closed walk?

Back

A walk that starts and ends at the same vertex.