Can a null graph be considered k-regular, for any k ? By null graph I mean a graph without any vertices. I did not find any mention of this anywhere. 

Looking at the definition of a k-regular graph it's obvious taht you can consider the empty graph k-regular for any k. Why? Because since it has no vertices the statement: "every vertex has degree k" is true for any k.   
But I am not sure how that helps and in what scenarios.   
