In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks.

1. v₀e₁v₁e₁₀v₅e₉v₂e₂v₁
2. v₄e₇v₂e₉v₅e₁₀v₁e₃v₂e₉v₅
3. v₂
4. v₅v₂v₃v₄v₅
5. v₂v₃v₄v₅v₂v₄v₃v₂
6. e₂e₈e₁₀e₃

(a)

In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks.

Given information:

Calculation:

We know that:

A walk from v to w is a finite sequence of alternatively adjacent vertices and edges of a graph.

A trail from v to w is a walk that does not contain a repeated edge.

A path from v to w is a trial that does not contain a repeated vertex.

A closed walk is a walk that starts and ends at the same vertex.

A circuit is a closed walk with at least one edge and no repeated edges.

A simple circuit is a circuit with no repeated vertices except for the first and last vertex.

We have: v0e1v1e10v5e9v2e2v1.

The walk v0e1v1e10v5e9v2e2v1 is a trial, because we note that the walk does not contain a repeated edge (as the edges are e1,e10,e9 and e2).

The walk v0e1v1e10v5e9v2e2v1 is not a path, because we not that the walk contains the vertex v₁ twice.

The walk v0e1v1e10v5e9v2e2v1 is not a closed walk, because the first vertex v₀ is different from the last vertex v₁

(b)

In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks.

(c)

In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks.

(d)

In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks.

(e)

In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks.

(f)

In the graph below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks.