stylistic:style_transfer, information:extraction
Regular graphs

The degree sum formula implies that every r {\displaystyle r} - regular graph with n {\displaystyle n} vertices has n r / 2 {\displaystyle nr/2} edges. Because the number of edges must be an integer, it follows that when r {\displaystyle r} is odd the number of vertices must be even. Additionally, for odd values of r {\displaystyle r}, the number of edges must be divisible by r {\displaystyle r}.