Java Program to Check whether a Graph is Bipartite using 2 Color Algorithm

This Java program is to Check whether Graph is a Bipartite using 2 Color Algorithm.In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint sets and such that every edge connects a vertex in to one in ; that is, and are each independent sets.
The two sets and may be thought of as a coloring of the graph with two colors: if one colors all nodes in blue, and all nodes in green, each edge has endpoints of differing colors, as is required in the graph coloring problem.In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle.

Here is the source code of the Java program to Check whether Graph is a Bipartite using 2 Color Algorithm. The Java program is successfully compiled and run on a Linux system. The program output is also shown below.

import java.util.InputMismatchException;

```
import java.util.Scanner;
```
```
public class CheckBipartite
```
```
{
```
```
    private int numberOfNodes;
```

    private static final int NO_OF_COLOR = 2;

```
 
```

    private boolean isSafe(int vertex,int[][] adjacencyMatrix, int [] colored, int color)

```
    {
```

        for (int destination = 1; destination <= numberOfNodes; destination++)

```
        {
```

            if (adjacencyMatrix[vertex][destination] == 1 && colored[destination] == color)

```
            {
```
```
                return false;
```
```
            }
```
```
        }
```
```
        return true;
```
```
    }
```
```
 
```

    private boolean checkBipartiteUtil(int adjacencyMatrix[][], int[] colored, int vertex)

```
    {
```
```
        if (vertex > numberOfNodes)
```
```
        {
```
```
            return true;
```
```
        }
```
```
 
```

        for (int colorNum = 1; colorNum <= NO_OF_COLOR; colorNum++)

```
        {
```

            if (isSafe(vertex, adjacencyMatrix, colored, colorNum))

```
            {
```

                colored[vertex] = colorNum;

                if (checkBipartiteUtil(adjacencyMatrix, colored, vertex + 1))

```
                {  
```
```
                    return true;
```
```
                }
```
```
                else
```
```
                {
```
```
                    return false;
```
```
                }
```
```
            }	
```
```
        }
```
```
        return false;
```
```
    }
```
```
 
```

    public boolean checkBipartite(int adjacencyMatrix[][])

```
    {
```
```
        boolean bipartite = true;
```

        numberOfNodes = adjacencyMatrix[1].length - 1;

        int[] colored = new int[numberOfNodes + 1];

```
 
```

        for (int vertex = 1; vertex <= numberOfNodes; vertex++)

```
        {
```
```
            colored[vertex] = 0;
```
```
        }
```
```
 
```

        if (!checkBipartiteUtil(adjacencyMatrix, colored, 1))

```
        {
```
```
            bipartite = false;
```
```
        }
```
```
        return bipartite;
```
```
    }
```
```
 
```

    public static void main(String... arg)

```
    {
```
```
        int number_of_nodes;
```
```
        Scanner scanner = null;
```
```
 
```
```
        try
```
```
        {
```

            System.out.println("Enter the number of nodes in the graph");

            scanner = new Scanner(System.in);

            number_of_nodes = scanner.nextInt();

```
 
```

            int adjacency_matrix[][] = new int[number_of_nodes + 1][number_of_nodes + 1];

            System.out.println("Enter the adjacency matrix");

            for (int i = 1; i <= number_of_nodes; i++)

```
            {
```

                for (int j = 1; j <= number_of_nodes; j++)

```
                {	
```

                    adjacency_matrix[i][j] = scanner.nextInt();

```
                }
```
```
            }
```
```
 
```

            for (int i = 1; i <= number_of_nodes; i++)

```
            {
```

                for (int j = 1; j <= number_of_nodes; j++)

```
                {	
```

                    if (adjacency_matrix[i][j] == 1 && adjacency_matrix[j][i] == 0)

```
                    {
```

                        adjacency_matrix[j][i] = 1;

```
                    }
```
```
                }
```
```
            }			
```
```
 
```

            CheckBipartite bipartite = new CheckBipartite();

            if (bipartite.checkBipartite(adjacency_matrix))

```
            {
```

                System.out.println("the given graph is bipartite");

```
            }
```
```
            else
```
```
            {
```

                System.out.println("the given graph is not bipartite");

```
            }
```
```
        }
```

        catch (InputMismatchException inputMismatch)

```
        {
```

            System.out.println("Wrong Input format");

```
        }
```
```
        scanner.close();
```
```
    }	
```
```
}
```

$javac CheckBipartite.java
$java CheckBipartite
 
Enter the number of nodes in the graph
6
Enter the adjacency matrix
0 1 0 1 0 1
1 0 1 0 1 0
0 1 0 1 0 1
1 0 1 0 1 0
0 1 0 1 0 1
1 0 1 0 1 0
the given graph is bipartite

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