This is a java program to generate a graph from given degree sequence. The degree sequence of an undirected graph is the non-increasing sequence of its vertex degrees.The degree sequence problem is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. A sequence which is the degree sequence of some graph, i.e. for which the degree sequence problem has a solution, is called a graphic or graphical sequence. As a consequence of the degree sum formula, any sequence with an odd sum, such as (3, 3, 1), cannot be realized as the degree sequence of a graph. The converse is also true: if a sequence has an even sum, it is the degree sequence of a multigraph. The construction of such a graph is straightforward: connect vertices with odd degrees in pairs by a matching, and fill out the remaining even degree counts by self-loops.

Here is the source code of the Java Program to Generate a Graph for a Given Fixed Degree Sequence. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

package com.hinguapps.combinatorial;

import java.util.ArrayList;

import java.util.List;

import java.util.Scanner;

public class GraphUsingDegreeSequence

`{`

Integer[][] adjecencyMatrix;

List<Integer> degreeSequence;

private void addEdges(Integer v, Integer e)

`{`

for (int i = 0; i < adjecencyMatrix.length && e > 0; i++)

`{`

if (degreeSequence.get(i) != 0)

`{`

adjecencyMatrix[v][i] = adjecencyMatrix[i][v] = 1;

Integer val = degreeSequence.get(i);

if (val > 0)

degreeSequence.set(i, val - 1);

`e--;`

`}`

`}`

`}`

public void generateGraph()

`{`

adjecencyMatrix = new Integer[degreeSequence.size()][degreeSequence

.size()];

for (int i = 0; i < adjecencyMatrix.length; i++)

`{`

for (int j = 0; j < adjecencyMatrix.length; j++)

`{`

adjecencyMatrix[i][j] = 0;

`}`

`}`

for (int i = 0; i < degreeSequence.size(); i++)

`{`

Integer e = degreeSequence.get(i);

degreeSequence.set(i, 0);

addEdges(i, e);

`}`

`}`

public void printGraph()

`{`

System.out.println("The matrix form of graph: ");

for (int i = 0; i < adjecencyMatrix.length; i++)

`{`

for (int j = 0; j < adjecencyMatrix.length; j++)

`{`

System.out.print(adjecencyMatrix[i][j] + " ");

`}`

System.out.println();

`}`

`}`

public static void main(String[] args)

`{`

Scanner sc = new Scanner(System.in);

System.out.println("Enter the number of vertices: ");

Integer n = sc.nextInt();

System.out

.println("Enter the Degree Sequence: <Degree sequence is always in non-increasing order>");

GraphUsingDegreeSequence gds = new GraphUsingDegreeSequence();

gds.degreeSequence = new ArrayList<Integer>();

while (n > 0)

`{`

gds.degreeSequence.add(sc.nextInt());

`n--;`

`}`

System.out.println("Entered degree sequence: "

+ gds.degreeSequence.toString());

gds.generateGraph();

gds.printGraph();

sc.close();

`}`

`}`

Output:

$ javac GraphUsingDegreeSequence.java $ java GraphUsingDegreeSequence Enter the number of vertices: 7 Enter the Degree Sequence: <Degree sequence is always in non-increasing order> 5 3 3 2 2 1 0 Entered degree sequence: [5, 3, 3, 2, 2, 1, 0] The matrix form of graph: 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

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