This Java program is to find the number of spanning trees in a Complete Bipartite graph. This can be calculated using the matrix tree theorem or Cayley’s formula.

Here is the source code of the Java program to ind the number of spanning trees in a Complete Bipartite graph. The Java program is successfully compiled and run on a Linux system. The program output is also shown below.

import java.util.Scanner;

public class NumOfSpanningBipartite

`{`

private int firstSetSize;

private int secondSetSize;

public int numberOfSpanningTree(int firstSetSize, int secondSetSize)

`{`

this.firstSetSize = firstSetSize;

this.secondSetSize = secondSetSize;

return (this.firstSetSize^(this.secondSetSize - 1)) *(this.secondSetSize ^ (this.firstSetSize -1));

`}`

public static void main(String...arg)

`{`

int m, n;

Scanner scanner = new Scanner(System.in);

System.out.println("enter the size of the bipartite graph (m and n)");

m = scanner.nextInt();

n = scanner.nextInt();

NumOfSpanningBipartite bipartite = new NumOfSpanningBipartite();

System.out.println(" the number of spanning trees are " + bipartite.numberOfSpanningTree(m, n));

scanner.close();

`}`

`}`

$javac NumOfSpanningBipartite.java $java NumOfSpanningBipartite enter the size of the bipartite graph (m and n) 2 2 the number of spanning trees are 9

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