# Simple Graph with 5 vertices of degrees 2, 3, 3, 3, 5

I'm taking a class in Discrete Mathematics, and one of the problems in my homework asks for a Simple Graph with 5 vertices of degrees 2, 3, 3, 3, and 5. How can I have more than 4 edges? I'm really confused, maybe I don't really understand what a "Simple Graph" means.

• What do you think the definition of "simple graph" is? – Randall Dec 3 '18 at 2:33
• Has no loops, no multi-edges. – Ayaan Siddiqui Dec 3 '18 at 2:34
• Have you considered the fact that they might have intended for you to state that such a graph cannot exist? – Boshu Dec 3 '18 at 2:36
• Since there are $5$ vertices, no vertex can have degree more than $4$. – the_fox Dec 3 '18 at 2:36
• Looks like professor made a typo then – Ayaan Siddiqui Dec 3 '18 at 2:36

Since you only have 5 vertices, it is not possible in a simple graph to have a maximum degree of more than $$5-1=4$$. Hence, such a simple graph as required does not exist.