Edge Sequence

graph-theory

Definition

Edge Sequence

Undirected: A sequence of edges of an undirected graph is called edge sequence if there exist vertices with:

where the vertices can be traversed from to in any order.

Directed: A sequence of edges of a directed graph is called edge sequence if, for any two consecutive edges (), the end node of matches the start node of . That is, there exists nodes sucht that:

Empty Edge Sequence

Empty Edge Sequence

An edge sequence of length is called empty edge sequence and does not contain any edges .

Kantenzug

todo

Kantenzug

A Kantenzug is an edge sequence where all edges are different, meaning each edges is only traversed once.

Path

Weg, Pfad, Bahn

Definition

Path

A path is an edge sequence where each vertex is only visited once.

Link to original

Loop

Kreis

Loop

An edge sequence is called loop if all vertices except are start and end nodes, different and and each edge only occurrs once.