Discrete Mathematics

Calculation of Degree of a Vertex
The computation of a degree of a vertex of a graph is just simple. Just count the number of edges start or incident on a particular vertex V in a graph is called the degree of a vertex. Or we can say that the degree of a vertex is the number of edges or arcs connected with it.
Important Note :
Pendent Vertex :
When the degree of a vertex is one (with only one edge connected), then it is known as Pendent Vertex.
Isolated Vertex : A vertex of degree zero is Isolated Vertex.
Let us find the degree of a vertex of some graph given below.

Example: Find the degree of each vertex of a graph given below.

Solution : The degree of each vertex in a graph is
Degree of a vertex 'a' = deg(a) = 3
Degree of a vertex 'b' = deg(b) = 2
Degree of a vertex 'c' = deg(c) = 2
Degree of a vertex 'd' = deg(d) = 3
Degree of a vertex 'e' = deg(e) = 1 (also Known as Pendent Vertex )
Degree of a vertex 'f' = deg(f) = 0 (also known as Isolated Vertex )
Degree of a vertex 'g' = deg(g) = 3