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

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Question: If a graph has 5 vertices and 7 edges, what is the maximum number of edges it can have?

Options:

Correct Answer: 15

Solution:

In a simple undirected graph, the maximum number of edges is given by the formula V(V-1)/2, which for 5 vertices is 5(5-1)/2 = 10.

If a graph has 5 vertices and 7 edges, what is the maximum number of edges it can have?

If a graph has 5 vertices and 7 edges, what is the maximum number of edges it can have?

Step 1: Understand what a vertex is. A vertex is a point in a graph where edges meet.
Step 2: Understand what an edge is. An edge is a line that connects two vertices.
Step 3: Identify how many vertices are in the graph. In this case, there are 5 vertices.
Step 4: Use the formula for the maximum number of edges in a simple undirected graph, which is V(V-1)/2, where V is the number of vertices.
Step 5: Substitute the number of vertices into the formula: V = 5, so we calculate 5(5-1)/2.
Step 6: Calculate (5-1) which equals 4.
Step 7: Multiply 5 by 4 to get 20.
Step 8: Divide 20 by 2 to get 10.
Step 9: Conclude that the maximum number of edges in a graph with 5 vertices is 10.

Graph Theory – Understanding the properties of graphs, including vertices and edges, and how to calculate the maximum number of edges in a simple undirected graph.
Combinatorial Mathematics – Applying combinatorial principles to determine the maximum connections (edges) possible between a set number of points (vertices).