This is a java program to check whether graph contains Eulerian Cycle. The criteran Euler suggested,

1. If graph has no odd degree vertex, there is at least one Eulerian Circuit.

2. If graph as two vertices with odd degree, there is no Eulerian Circuit but at least one Eulerian Path.

3. If graph has more than two vertices with odd degree, there is no Eulerian Circuit or Eulerian Path.

1. If graph has no odd degree vertex, there is at least one Eulerian Circuit.

2. If graph as two vertices with odd degree, there is no Eulerian Circuit but at least one Eulerian Path.

3. If graph has more than two vertices with odd degree, there is no Eulerian Circuit or Eulerian Path.

Here is the source code of the Java Program to Check Whether an Undirected Graph Contains a Eulerian Path. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

package com.sanfoundry.graph;

import java.util.InputMismatchException;

import java.util.Scanner;

public class UndirectedEulerPath

`{`

private int[][] adjacencyMatrix;

private int numberOfNodes;

public UndirectedEulerPath(int numberOfNodes, int[][] adjacencyMatrix)

`{`

this.numberOfNodes = numberOfNodes;

this.adjacencyMatrix = new int[numberOfNodes + 1][numberOfNodes + 1];

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

`{`

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

`{`

this.adjacencyMatrix[sourceVertex][destinationVertex] = adjacencyMatrix[sourceVertex][destinationVertex];

`}`

`}`

`}`

public int degree(int vertex)

`{`

int degree = 0;

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

`{`

if (adjacencyMatrix[vertex][destinationvertex] == 1

|| adjacencyMatrix[destinationvertex][vertex] == 1)

`{`

`degree++;`

`}`

`}`

return degree;

`}`

public int countOddDegreeVertex()

`{`

int count = 0;

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

`{`

if ((degree(node) % 2) != 0)

`{`

`count++;`

`}`

`}`

return count;

`}`

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();

`}`

`}`

`// make the graph undirected`

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;

`}`

`}`

`}`

DirectedEulerianCircuit path = new DirectedEulerianCircuit(number_of_nodes,

adjacency_matrix);

int count = path.countOddDegreeVertex();

if (count == 0)

`{`

System.out

.println("As the graph has no odd degree vertex, there is at least one Eulerian Circuit.");

`}`

else if (count == 2)

`{`

System.out

.println("As the graph as two vertices with odd degree, there is no Eulerian Circuit but at least one Eulerian Path.");

`}`

`else`

`{`

System.out

.println("As the graph has more than two vertices with odd degree, there is no Eulerian Circuit or Eulerian Path.");

`}`

`}`

catch (InputMismatchException inputMismatch)

`{`

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

`}`

scanner.close();

`}`

`}`

Output:

$ javac UndirectedEulerPath.java $ java UndirectedEulerPath Enter the number of nodes in the graph 4 Enter the adjacency matrix 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 As the graph as two vertices with odd degree, there is no Eulerian Circuit but at least one Eulerian Path.

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