Question

find the degree of each vertex in the graph
complete the following table
vertex | a | b | c | d | e | f
degree of vertex | | | | | |
(type whole numbers )

Explanation:

Step1: Recall the degree formula

The degree of a vertex is the number of edges incident to it. For a loop at a vertex \(v\), it contributes \(2\) to the degree of \(v\).

Step2: Calculate degree of vertex \(A\)

Vertex \(A\) is connected to \(C\) by one edge. So, \(\text{deg}(A)=1\).

Step3: Calculate degree of vertex \(B\)

Vertex \(B\) has a loop (counts as \(2\) edges) and is connected to \(C\) by one edge. So, \(\text{deg}(B)=2 + 1=3\).

Step4: Calculate degree of vertex \(C\)

Vertex \(C\) is connected to \(A\), \(B\) and \(D\). So, \(\text{deg}(C)=3\).

Step5: Calculate degree of vertex \(D\)

Vertex \(D\) is connected to \(C\), \(E\) and \(F\). So, \(\text{deg}(D)=3\).

Step6: Calculate degree of vertex \(E\)

Vertex \(E\) is connected to \(D\) and \(F\). So, \(\text{deg}(E)=2\).

Step7: Calculate degree of vertex \(F\)

Vertex \(F\) is connected to \(D\) and \(E\). So, \(\text{deg}(F)=2\).

Answer:

Vertex	A	B	C	D	E	F