Contents

- 1 What is the difference between path and walk?
- 2 What is Path and Trail?
- 3 Is a cycle a walk?
- 4 What is a trail in discrete math?
- 5 Is every path a walk?
- 6 Is every walk a trail?
- 7 What is a closed walk in graph theory?
- 8 What is a closed path called?
- 9 What is the weight of an edge?
- 10 Is a closed walk a cycle?
- 11 Is self loop a cycle?
- 12 What is a simple cycle?
- 13 What is simple circuit in discrete mathematics?
- 14 Is a single vertex a walk?
- 15 What does trail mean?

## What is the difference between path and walk?

An infinite walk is a sequence of edges of the same type described here, but with no first or last vertex, and a semi-infinite walk (or ray) has a first vertex but no last vertex. A trail is a walk in which all edges are distinct. A path is a trail in which all vertices (and therefore also all edges) are distinct.

## What is Path and Trail?

A trail is a walk with no repeated edge. A path is a walk with no repeated vertex. A u, v-walk, u, v- trail, u, v- path is a walk, trail, path, respectively, with first vertex u and last vertex v. If u = v then the u, v-walk and u, v- trail is closed.

## Is a cycle a walk?

A cycle of length n is a closed walk of length n,n ~ 3, in which the vertices xo, xl, ,Xn- l are all different. In specifying a path or cycle, it is sufficient to list only the sequence of vertices, because the edges are then uniquely determined.

## What is a trail in discrete math?

A trail is a walk,,,, with no repeated edge. The length of a trail is its number of edges. A – trail is a trail with first vertex and last vertex, where and. are known as the endpoints.

## Is every path a walk?

2 Answers. The thing that stops walks from being paths is loops. So you have to show that if there is one or more loops on a walk, then you can safely remove them all and still have a walk. That walk would then be a path.

## Is every walk a trail?

If the edges in a walk are distinct, then the walk is called a trail. In this way, every path is a trail, but not every trail is a path. Nowadays, when stated without any qualification, a path is usually understood to be simple, meaning that no vertices (and thus no edges) are repeated.

## What is a closed walk in graph theory?

Closed walk -A walk is said to be a closed walk if the starting and ending vertices are identical i.e. if a walk starts and ends at the same vertex, then it is said to be a closed walk.

## What is a closed path called?

â€¦than once is called a circuit, or a closed path. A circuit that follows each edge exactly once while visiting every vertex is known as an Eulerian circuit, and the graph is called an Eulerian graph.

## What is the weight of an edge?

Example: The weight of an edge can represent: Cost or distance = the amount of effort needed to travel from one place to another. Capacity = the maximim amount of flow that can be transported from one place to another.

## Is a closed walk a cycle?

A closed walk is a walk with the same endpoints, i.e., v0 = vk. A cycle is a closed walk with no repeated vertices except for the endpoints.

## Is self loop a cycle?

A self – loop or loop is an edge between a vertex and itself. An undirected graph without loops or multiple edges is known as a simple graph. A cycle is a closed path, i.e. a path combined with the edge (vk,v1).

## What is a simple cycle?

A simple cycle is a cycle with no repeated vertices (except for the beginning and ending vertex). Remark: If a graph contains a cycle from v to v, then it contains a simple cycle from v to v.

## What is simple circuit in discrete mathematics?

Path. A path is a sequence of vertices with the property that each vertex in the sequence is adjacent to the vertex next to it. A path that does not repeat vertices is called a simple path. Circuit. A circuit is path that begins and ends at the same vertex.

## Is a single vertex a walk?

2 Answers. A graph is connected if every pair of vertices in the graph can be connected by a path. By definition a single vertex is connected to itself by the trivial path. Hence, it is connected.

## What does trail mean?

1a(1): a track made by passage especially through a wilderness. (2): a marked or established path or route especially through a forest or mountainous region. b: a trace or mark left by something that has passed or been drawn along: scent, track a trail of blood.