Question

Is there a simple graph with degree sequence (1, 3, 3, 3, 5, 6, 6)?

Answer 1

Let G be a simple graph having degree sequence (1, 3, 3, 3, 5, 6, 6)

Clearly G has 7 vertices

since 2 vertices of degree 6, they are adjacent to the remaining 6 vertices

Therefore, every vertex of G has degree atleast 2

Hence, no vertex of G has degree 1

or

There is no simple graph having degree sequence (1, 3, 3, 3, 5, 6, 6)

Answer 2

Answer:

      There is no simple graph having a degree sequence (1,3,3,4,5,6,6)

Step-by-step explanation:

• Let G be a simple graph having a degree sequence (1, 3, 3, 3, 5, 6).
• Clearly, G has 7 vertices.
• since 2 vertices of degree 6, they are adjacent to the remaining 6 vertices.
• Therefore, every vertex of G has a degree of at least 2.
• Hence, no vertex of G has degree 1.
• There is no simple graph having a degree sequence (1, 3, 3, 3, 5, 6, 6)