Degree of Vertex

The degree of a vertex v in this graph G, written deg (v), is equal to the number of edges in G which contain v, that is, which are incident on v. Since each edge is counted twice in counting the degrees of the vertices of G, The degree of vertex refers the the number of edge incident in a graph. The number of graph edges which touch in a graph is the degree of vertex.In a graph the minimum degree of vertex is denoted by G and denoted by σG and maximum vertex is denoted by ΔG
Theorem of Degree of Vertex

The Degree sum in the vetices of  graph G is equal to twice the number of edges in G.

degree of vertex

 In a graph the vertex of graph is odd  node if its vertex degree is odd.Here this graph has 10 vertices hence its degree is even

The number associated with each vertex is its degree;it is  defined to be the number of edges that enter or exit from it—thus, a loop contributes 10 to the degree of its vertex.The vertices of the simple graph shown in the diagram all have a degree of 10.In the above diagram here the maximum degree is 3 and minimum degree is 7
Degree Formulae

In a graph G={V, E} , the degree sum formulae is given by:

Σ Deg (v) =2 (E) , here E is the number of edge of graph.In a graph the vertices are in a ordered list that is defined to be the degree sequence.This formulae implies number of vertices which are even and odd degree.
Conclusion of Degree of Vertex

Degree of vertex is very important part of a graph  family because it represents them. Degree of vertex is also defined to be its Valency. and also known to be isolated vertex.