walk

• a sequence of 1 or more vertices, (x0, x1,...,xk) such that each vertex has an edge to the next one

• can have repeating vertices or edges

• closed walk is a walk that starts and ends in the same vertex

• cycle is a

  • closed walk of length at least 1
  • with no repeating edges and no repeating vertices (except for the fact that the first is the same as the last)

  note: in an undirected graph, this means that a cycle has the length at least 3

• length of a walk is the number of edges along it, or, equivalently, the number of vertices minus one
• cost of a walk is ****the sum of the costs of the edges that form that walk

• a walk of length 0 is allowed (it has one vertex (so the starting vertex is the same as the destination vertex) and zero edges)
• a length 0 walk has cost 0

path

• a walk with no repeating vertices

adjacency

• vertex y is adjacent to vertex x if there is an edge from x to y

incidency

• vertex x is incident to edge e if x is an endpoint of e

accessible