Question

The number of edges incident on a vertex is referred as​

Answer 1

Answer:

Recall that the degree of a vertex is the number of edges incident to it. Since every edge must have two vertices that define it, an equivalent definition for the degree of a vertex v is the number of neighbors or the number of vertices adjacent to it.

Explanation:

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Answer 2

The number of edges incident on a vertex is referred as the degree of the vertex.

• In graph theory, the degree of a vertex is the number of edges incident to it. It can also be defined as the number of edges that are connected to a vertex.
• A vertex with a high degree is known as a high-degree vertex, and a vertex with a low degree is known as a low-degree vertex.
• A vertex with a degree of 0 is known as an isolated vertex.
• The degree of a vertex is an important property of a graph, and it is used in a number of graph algorithms and analyses.
• For example, in a graph with n vertices, the sum of all vertex degrees is equal to twice the number of edges in the graph.
• This property is known as the handshaking lemma and it is used in a number of graph theoretical proofs.
• Additionally, the degree of a vertex can be used to determine if a graph is regular (all vertices have the same degree) or irregular (vertices have different degrees).
• In summary, the degree of a vertex is the number of edges that are incident to it, it is an important property of a graph, and it is used in many graph-theoretical concepts and algorithms.

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