What is the maximum number of edges in a bipartite graph having 10 vertices?Select one:a.24b.21c.25d.16
Question
What is the maximum number of edges in a bipartite graph having 10 vertices?
Select one:
- a. 24
- b. 21
- c. 25
- d. 16
Solution
A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set.
The maximum number of edges in a bipartite graph can be found when the number of vertices in the two sets is as equal as possible.
Given that the total number of vertices is 10, we can divide them into two sets of 5 vertices each for maximum edges.
The maximum number of edges in a bipartite graph is given by the formula (n/2) * (n - n/2), where n is the total number of vertices.
Substituting n = 10 in the formula, we get:
(10/2) * (10 - 10/2) = 5 * 5 = 25
So, the maximum number of edges in a bipartite graph having 10 vertices is 25.
Therefore, the correct answer is c. 25.
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