If g is a simple graph with 15 edges?

If ( g ) is a simple graph with 15 edges, the maximum number of vertices ( n ) it can have can be determined using the formula for the maximum number of edges in a simple graph, which is given by ( \frac{n(n-1)}{2} ). Solving the inequality ( \frac{n(n-1)}{2} \geq 15 ) yields ( n(n-1) \geq 30 ). The smallest integer ( n ) satisfying this is ( n = 6 ), as ( 6(5) = 30 ). Thus, ( g ) can have up to 6 vertices, but it may also have fewer vertices depending on its specific structure.