Q98 / 170 · Manipal (MET) 2021 · Mathematics

In a simple regular graph, total degree is 28 . If the graph has more than one cycle in it, then the degree of each vertex is

  • A
    2
  • Correct answer
    B
    4
  • C
    7
  • D
    14

Solution

Total degree $=$ number of vertices $\times$ degree $=4 \times 7$ or $2 \times 14$ If there are 14 vertices each of degree 2 , then graph is a cycle. Hence, there are 7 vertices and each of degree 4 .

Hence, the correct answer is option: 'B'.

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