Is there a 5-regular graph of order 7? How can I decide  if there is  a 5-regular graph of order 7? 
Some hints or tips would be appreciated. This question arises in studying for a graph theory course.

Suppose $G$ is a $5$-regular graph of order $7$. Let $\bar G$ be the complementary graph: same vertices, but two vertices are joined by an edge in $\bar G$ just in case they are not joined by an edge in $G$. Can you see that $\bar G$ is a $1$-regular graph of order $7$? Is that possible? Try to draw it.
