What is an incident edge? [closed]

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Two edges of a graph are called adjacent (sometimes coincident) if they share a common vertex. Two arrows of a directed graph are called consecutive if the head of the first one is at the nock (notch end) of the second one. Similarly, two vertices are called adjacent if they share a common edge (consecutive if they are at the notch and at the head of an arrow), in which case the common edge is said to join the two vertices. An edge and a vertex on that edge are called incident.

I don't understand this definition. Could someone give an example of an incident edge? A schematic representation would be helpful.

Answer 1

Let G = (V, E) be an undirected graph, where V is the set of vertices and E is the set of (undirected) edges. Let u, v ∈ V be vertices of G. Let e = {u, v} ∈ E be an edge of G.

Then e = {u, v} is incident to u and v, or joins u and v. Similarly, u and v are incident to e.

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You can have more info at http://www.proofwiki.org/wiki/Definition:Incident.

Answer 2

The term Incident edge is used to give a relation in between an edge and vertex, which is different from concept of Adjacency (Relation between 2 vertices).

Example

• For example Adjacent vertex of 11 are 7,5,2,9,10
• But concept of Incidence is placed between and edge and vertex, thus Incident edge a incidents on vertex 11 from vertex 7, same way incident edge d incidents from vertex 11 and incidents on vertex 9.

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Since it is a Digraph
Here In Degree of vertex 11 is 2, whereas Out Degree of vertex 11 is 3.
But if it could be a Undirected Graph then this concept is not so significant, because adjacency and incidence of a vertex becomes same.

In Digraphs it is associated with In-Degree and Out-Degree of a vertex.
Whereas in Undirected graphs there remains no concept of Degree of incidence and we can say that vertex and the edge both are incident on each other.

Answer 3

A (directed) edge has a start vertex and an end vertex (which are not necessarily distinct). The term incident (as defined in your quote) means the edge together with either its start vertex or its end vertex.

It's common, for instance, to talk about "a vertex and an incident edge" meaning any edge that has the given vertex as either the start or end of the edge (or both).