Discrete Math Notes:
Chapter 6: Graphs and Trees
6.4 Walks, trails, circuits, paths, and cycles
Walk, an undirected graph G is a sequence of alternating vertices and edges that starts and ends with a vertex
Iength of a walk, the number of edges in the walk.
open walk, a walk in which the first and last vertices are not the same
closed walk, a walk in which the first and last vertices are the same.
Overview:
Example of a Walk in an Undirect Graph
Undirected graph:
Walk A.E,CB.E.A
This walk has length 5. There are 6 edges in the walk. including repetitions.
This walk is a closed wall because the first and last vertices are the same
Captions
1. A walk in an undirected graph starts at vertex A and follows the edge {A, E}. The walk so far is(A,E,... 2. Then the walk proceeds along edges {E, B} but can not continue from B to D because {B, D} is not an edge.A,E,B,D) is not a walk 3. The walk (A, E, B, C) is a walk of length 3. There are three edges in the walk. 4. The sequence (A) consisting of a single vertex is a walk of length 0. The walk has zero edges 5. The walk (A, E, C, B, E, A) is a walk of length 5. There are five edges, including repetitions. Edge {A E} occurs twice in the walk. 6.AE,C,B,E,A is a closed walk because the first and last vertices are the sa