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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.

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

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