Let $G$ be a simple undirected graph on $n=3x$ vertices $(x \geq 1)$ with chromatic number $3$, then maximum number of edges in $G$ is
Ok nx is fine. Only when we partition the vertex set into three disjoint non empty sets with x as each of their cardinality.
But no where in the question is it supposed that it should be the case, that all the vertex partitions need to have the same cardinality. How do we assume this? Just on the basis of the indication that n=3x?
@GO Classes sir?
Try with 3 vertex (x= 1) edges= 3*1 =3, and 6 vertex(x=2) = 6*2= 12 edges( all edges are bidirection )
Bdw in previous image if you count edges then that will be 13 .(use common sence )
can be checked with x=2, so it will be a 6 vertex graph
same as the graph shown in the comment by @Anu007