Walks, Paths and Cycles

Abstract

A walk in a graph G is a finite sequence of vertices x₀, x₁, ..., x _n and edges a₁, a₂, ..., a _n of G:

$$ x_0 ,a_1 ,x_1 ,a_2 ,...,a_n ,x_n , $$

where the endpoints of a _i are x_i−1 and x _i and x _i for each i . A simple walk is a walk in which no edge is repeated. If it is desired to specify the terminal vertices, the above walk is called an x₀x _n -walk. The length of a walk is its number of edges.