If a graph has 5 vertices and 7 edges, what is the maximum number of edges in a

If a graph has 5 vertices and 7 edges, what is the maximum number of edges in a complete graph with 5 vertices?

If a graph has 5 vertices and 7 edges, what is the maximum number of edges in a complete graph with 5 vertices?

Step 1: Understand what a complete graph is. A complete graph is a graph where every pair of distinct vertices is connected by a unique edge.
Step 2: Identify the number of vertices in the graph. In this case, we have 5 vertices.
Step 3: Use the formula for the maximum number of edges in a complete graph, which is V * (V - 1) / 2, where V is the number of vertices.
Step 4: Substitute the number of vertices into the formula. Here, V = 5, so we calculate 5 * (5 - 1) / 2.
Step 5: Perform the calculation: 5 * (4) / 2 = 20 / 2 = 10.
Step 6: Conclude that the maximum number of edges in a complete graph with 5 vertices is 10.

Graph Theory – Understanding the properties of graphs, including vertices and edges, and the concept of complete graphs.
Combinatorial Formulas – Applying the formula for the maximum number of edges in a complete graph, which is V*(V-1)/2.