The question is to write two boolean expressions per set of graphs that differentiate between them. The domain for the expression should be all vertices in the given graph. Also, $E(x,y) =$ "there is an undirected edge between $x$ and $y$".
The only difference I found between 1.1 and 1.2 was that 1.2 has an additional vertex that has an edge with the last vertex.
For 1.1: $\exists x,y,z (E(x,y) \land E(y,z) \land x \ne y \ne z)$
For 1.2, $\exists x,y,z,n (E(x,y) \land E(y,z) \land E(z,n) \land x \ne y \ne z \ne n)$
The difference I found here was that in 2.1, if the first vertex is connected to a second vertex and the second vertex is connected to a third vertex, then the first vertex is not connected to the third vertex. However, in 2.2, all vertices are connected to each other.
For 2.1: $\forall x,y,z (x \ne y \ne z \rightarrow E(x,y) \land E(y,z) \land \lnot E(x,z))$
For 2.2: $\forall x,y (x \ne y \rightarrow E(x,y))$
Am I interpreting these graphs correctly through my boolean expressions. If I am, then is there a more concise or logical way to represent these graphs?