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

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Question: If a graph has 5 vertices and 7 edges, what is the maximum number of edges in a simple undirected graph?

Options:

Correct Answer: 10

Solution:

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

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

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

Step 1: Understand what a simple undirected graph is. It is a graph without loops or multiple edges between the same pair of vertices.
Step 2: Identify the number of vertices (V) in the graph. In this case, V = 5.
Step 3: Use the formula for the maximum number of edges in a simple undirected graph, which is V(V-1)/2.
Step 4: Substitute the value of V into the formula: 5(5-1)/2.
Step 5: Calculate (5-1) which equals 4.
Step 6: Multiply 5 by 4 to get 20.
Step 7: Divide 20 by 2 to get 10.
Step 8: Conclude that the maximum number of edges in a simple undirected graph with 5 vertices is 10.

Graph Theory – Understanding the properties of simple undirected graphs, including the relationship between vertices and edges.
Combinatorial Mathematics – Applying combinatorial formulas to determine the maximum number of edges based on the number of vertices.