 Problem Statement

A graph has 12 edges and 6 nodes, each of which has degree of 2 or 5. How many nodes
are there of each degree?
 Relevant Equations

handshake theorem.
2m = summation of degree of each vertice where m = # of edges
there must be an even number of vertices of odd degree, and from the handshake theorem, 2m = 2(12) = 24
the only way we can get this from 6 vertices using 2 and 5 is:
4 vertices of degree 5, 2 vertices of degree 2
does this seem correct??
the only way we can get this from 6 vertices using 2 and 5 is:
4 vertices of degree 5, 2 vertices of degree 2
does this seem correct??