Answer:
7
Explanation:
Let S be the set of all graphs having vertex set \{1,2,3,4\}. The relation \rho is defined over S such that
the graphs G and H are equivalent provided that they have same number of edges. Then, the number of equivalence classes depends on how many edges can be there in the vertex set \{1,2,3,4\} .
The number of edges is 0 forms a disconnected graph which makes an equivalent class.
The graphs of 1 edge makes an equivalent class.
The graphs of 2 edges makes an equivalent class.
The graphs of 3 edges makes an equivalent class.
The graphs of 4 edges makes an equivalent class.
The graphs of 5 edges makes an equivalent class.
In similar way, the only graph of 6 edges is complete graph which forms another equivalent class.
Hence,the total number of equivalent classes is 7.