The answer is option C.
Explanation:
For node = 1 : for node = 1, there is only one graph is possible.
For node = 2 : for node = 2, there are two distinct graph is possible. Either two nodes are isolated or connected.
For node = 3: for node = 3, there are four distinct graph is possible. Lets see why four graphs are possible. If we represent a graph using adjacency matrix, then for simple graph all diagonal elements are zero. So, for 3*3 square matrix there ar 6 available choices are there. But here we want only distinct graph so the choice will 6/2=3, because for this example, edge between (1,2) is similar to edge between (2,1). So, there are 3 distinct graph is possible with connected edges, And one graph is possible when all the vertices are disconnected. So total number of graph for node = 3 is (3+1)=4.
The number of distinct simple graphs with up to three nodes is
= (1+2+4)=7.