We can solve this type of problem by assuming graph which holds true for their constraint given,

For statement 1 and 2 , graph contain six vertices and have degree = 2 ( for each node )

simple graph , graph which have no multiple edges and self loop is known as simple graph but it can be connected or not.

each node have two degree means , each node is connected with two different nodes , because simple graph doesn't have multiple edges or self loop.

Then graph have to be cyclic like [ A - B - C - D - E - F - A ] , all have degree equals to two.

Hence statement one is true.

Second, euler circuit : start from any node , traverse each edge exactly once and come back to the starting node is know as euler circuit, which is true for this graph, hence statement 2 is correct.

Statement 3 : you can surely draw a graph, which have no self loop and no multiple edges, and have degree equals to three , and it is disconnected.