Java Program to Check whether Graph is a 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