A bigraph or bipartite graph G is a graph whose vertex set V(G) can be partitioned into two disjoint vertex sets such that there is no edge between the same vertex set [ 1,2]. These graphs are said to be 2-colorable graphs that can be colored using only two colors [ 3]. This article checks if a given graph is bipartite or not using Java implementation. The complete bipartite graph or biclique is a graph in which every vertex in one set is incident with every vertex in the other set. The bipartite graph is shown inFigure figure 1. The complete bipartite graphs are shown in figures 2 and 3 [ 4,5]. The bipartite graphs are applied in social networks and search engines. These graphs are also used to represent the binary relations between two object types [ 6,7].

The java implementation to check if the given graph is bipartite or not is given below. The color assignment of the bipartite graph is also printed.

import java.util.*;

public class bipartiteCheck

{

static List<List<Integer>> adjList;

static void edgeAddition(int a, int b)

{

adjList.get(a).add(b);

adjList.get(b).add(a);

}

static boolean bipartiteCheckEx(int n)

{

// not colored &#x02013; &#x02018;n&#x02019;

// colored blue &#x02013; &#x02018;b&#x02019;

// colored yellow &#x02013; &#x02018;y&#x02019;

char colorAssignment[ ] = new char[n];

for (int j = 0; j < n; j++)

colorAssignment[j] = 'n';

Queue<Integer> queue = new LinkedList<>();

queue.add(0);

colorAssignment[ ] = 'b';

while (!queue.isEmpty())

{

int h = queue.poll();

char ch = colorAssignment[h];

for(int g : adjList.get(h))

{

if(colorAssignment[g] == ch) return false;

if(colorAssignment[g] == 'n')

{

if(ch == 'b')

colorAssignment[g] = 'y';

else

colorAssignment[g] = 'b';

queue.add(g);

}

}

}

for (int j = 0; j < n; j++)

System.out.println("color["+j+"]="+colorAssignment[j]);

return true;

}

public static void main(String ax[ ]){

int n = 4;

adjList = new ArrayList<>();

for(int j = 0; j < n; j++)

adjList.add(new ArrayList<>());

edgeAddition(0, 1);

edgeAddition(0, 2);

edgeAddition(0, 3);

edgeAddition(1, 3);

edgeAddition(2, 3);

System.out.println("Graph 1");

if(bipartiteCheckEx(n))

System.out.println("Bipartite graph");

else

System.out.println("Not a bipartite graph");

adjList = new ArrayList<>();

for(int i = 0; i < n; i++)

adjList.add(new ArrayList<>());

edgeAddition(0, 1);

edgeAddition(0, 2);

edgeAddition(1, 3);

edgeAddition(2, 3);

System.out.println("Graph 2");

if(bipartiteCheckEx(n))

System.out.println("Bipartite graph ");

else

System.out.println("Not a bipartite graph");

n = 8;

adjList = new ArrayList<>();

for(int j = 0; j < 8; j++)

adjList.add(new ArrayList<>());

edgeAddition(0, 1);

edgeAddition(0, 2);

edgeAddition(0, 4);

edgeAddition(3, 1);

edgeAddition(3, 2);

edgeAddition(3, 7);

edgeAddition(5, 1);

edgeAddition(5, 4);

edgeAddition(5, 7);

edgeAddition(6, 2);

edgeAddition(6, 4);

edgeAddition(6, 7);

System.out.println("Graph 3");

if(bipartiteCheckEx(n))

System.out.println("Bipartite graph ");

else

System.out.println("Not a bipartite graph");

n = 8;

adjList = new ArrayList<>();

for(int j = 0; j < 8; j++)

adjList.add(new ArrayList<>());

edgeAddition(0, 1);

edgeAddition(0, 2);

edgeAddition(0, 4);

edgeAddition(3, 1);

edgeAddition(3, 2);

edgeAddition(3, 7);

edgeAddition(3, 5);

edgeAddition(5, 1);

edgeAddition(5, 4);

edgeAddition(5, 7);

edgeAddition(6, 2);

edgeAddition(6, 4);

edgeAddition(6, 7);

edgeAddition(1, 7);

System.out.println("Graph 4");

if(bipartiteCheckEx(n))

System.out.println("Bipartite graph ");

else

System.out.println("Not a bipartite graph");

n = 8;

adjList = new ArrayList<>();

for(int j = 0; j < 8; j++)

adjList.add(new ArrayList<>());

edgeAddition(0, 5);

edgeAddition(0, 6);

edgeAddition(0, 7);

edgeAddition(1, 5);

edgeAddition(1, 6);

edgeAddition(1, 7);

edgeAddition(2, 5);

edgeAddition(2, 6);

edgeAddition(2, 7);

edgeAddition(3, 5);

edgeAddition(3, 6);

edgeAddition(3, 7);

edgeAddition(4, 5);

edgeAddition(4, 6);

edgeAddition(4, 7);

System.out.println("Graph 5");

if(bipartiteCheckEx(n))

System.out.println("Bipartite graph ");

else

System.out.println("Not a bipartite graph");

}

}

The execution and the result of the Java program is shown inFigure figure 4. The graphs 1, 2, 3, 4 and 5 are given as the inputs and the results are shown in figures from 5 to 9 respectively. The program outputs the color assignments of the bipartite graphs.

This research presented the method to check if the given graph is bipartite or not. The color assignment of the bipartite graph is also obtained and the method is executed on some of the sample graphs and the results are presented. New strategies will be developed for bipartite graphs using the various soft computing methods [ 8,9,10,11,12,13,14,15,16].