Maximum number of edges in Bipartite graph
Given an integer N which represents the number of Vertices. The Task is to find the maximum number of edges possible in a Bipartite graph of N vertices.
Bipartite Graph:
- A Bipartite graph is one which is having 2 sets of vertices.
- The set are such that the vertices in the same set will never share an edge between them.
Examples:
Input: N = 10
Output: 25
Both the sets will contain 5 vertices and every vertex of first set
will have an edge to every other vertex of the second set
i.e. total edges = 5 * 5 = 25Input: N = 9
Output: 20
Approach: The number of edges will be maximum when every vertex of a given set has an edge to every other vertex of the other set i.e. edges = m * n where m and n are the number of edges in both the sets. in order to maximize the number of edges, m must be equal to or as close to n as possible. Hence, the maximum number of edges can be calculated with the formula,
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function to return the maximum number // of edges possible in a Bipartite // graph with N vertices int maxEdges(int N) { int edges = 0; edges = floor((N * N) / 4); return edges; } // Driver code int main() { int N = 5; cout << maxEdges(N); return 0; } |
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Java
// Java implementation of the approach class GFG { // Function to return the maximum number // of edges possible in a Bipartite // graph with N vertices public static double maxEdges(double N) { double edges = 0; edges = Math.floor((N * N) / 4); return edges; } // Driver code public static void main(String[] args) { double N = 5; System.out.println(maxEdges(N)); } } // This code is contributed by Naman_Garg. |
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Python3
# Python3 implementation of the approach # Function to return the maximum number # of edges possible in a Bipartite # graph with N vertices def maxEdges(N) : edges = 0; edges = (N * N) // 4; return edges; # Driver code if __name__ == "__main__" : N = 5; print(maxEdges(N)); # This code is contributed by AnkitRai01 |
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C#
// C# implementation of the approach using System; class GFG { // Function to return the maximum number // of edges possible in a Bipartite // graph with N vertices static double maxEdges(double N) { double edges = 0; edges = Math.Floor((N * N) / 4); return edges; } // Driver code static public void Main() { double N = 5; Console.WriteLine(maxEdges(N)); } } // This code is contributed by jit_t. |
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PHP
<?php // PHP implementation of the approach // Function to return the maximum number // of edges possible in a Bipartite // graph with N vertices function maxEdges($N) { $edges = 0; $edges = floor(($N * $N) / 4); return $edges; } // Driver code $N = 5; echo maxEdges($N); // This code is contributed by ajit. ?> |
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Output:
6
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