Question

In a regular graph of fifteen vertices the sum of the degree of vertices is sixty. Then the degree of each vertex is_.
A. Five
B. Three
C. Four
D. Two

Answer 1

Hint:- Submission of degree of vertices is equal to $2E$ where $E$ is the number of edges and value of $2E$ is given as $60$.

Complete step-by-step solution -
Given is sum of the degree of $15$ vertices$ = 60$
Let $x$ be the degree of each vertices
According to sum of degree theorem: Submission of degree of vertices is equals to $2E$
It means ${d_{_1}} + {d_2} + {d_3}........ + {d_{15}} = 2E$
$
  \therefore 15 \times x = 60 \\
  x = 4 \\
$
Therefore degree of each vertices is $4$
Hence the correct option is C.

Note:- In this question we have considered $x$ be the degree of each vertex. After that we applied the values in the submission of degree formula and found that the degree of each vertex is four.