Graph Isomorphism

Graph isomorphism is a topic in graph theory that deals with determining whether two graphs are isomorphic, i.e., whether they have the same structure.

A graph isomorphism is a one-to-one mapping between the vertices of two graphs that preserves the edge structure.

Determining graph isomorphism is a challenging problem and is often studied in the context of algorithm design and complexity theory.

There are various algorithms to check for graph isomorphism, including the Weisfeiler-Lehman algorithm, the Nauty algorithm, and the Individualization-Refinement algorithm.

Here's an example Java code that demonstrates checking graph isomorphism:

1// Example code for checking graph isomorphism
2
3class Main {
4  public static void main(String[] args) {
5    // Create two example graphs
6    int[][] graph1 = {
7      {0, 1, 1},
8      {1, 0, 1},
9      {1, 1, 0}
10    };
11
12    int[][] graph2 = {
13      {0, 1, 0},
14      {1, 0, 1},
15      {0, 1, 0}
16    };
17
18    if (isIsomorphic(graph1, graph2)) {
19      System.out.println("The two graphs are isomorphic.");
20    } else {
21      System.out.println("The two graphs are not isomorphic.");
22    }
23  }
24
25  private static boolean isIsomorphic(int[][] graph1, int[][] graph2) {
26    // Logic for checking graph isomorphism
27    // Replace with your own implementation
28    return true;
29  }
30}

The code creates two example graphs and uses a placeholder function isIsomorphic to check if they are isomorphic. In the code, replace the isIsomorphic function with the logic for checking graph isomorphism.

Feel free to modify the code and test it with different graphs to understand the concept of graph isomorphism better.

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}

class Main {

  public static void main(String[] args) {

    // replace with your Java logic here

    System.out.println("Checking graph isomorphism...");

​

    // Create two example graphs

    int[][] graph1 = {

      {0, 1, 1},

      {1, 0, 1},

      {1, 1, 0}

    };

​

    int[][] graph2 = {

      {0, 1, 0},

      {1, 0, 1},

      {0, 1, 0}

    };

​

    if (isIsomorphic(graph1, graph2)) {

      System.out.println("The two graphs are isomorphic.");

    } else {

      System.out.println("The two graphs are not isomorphic.");

    }

  }

​

  private static boolean isIsomorphic(int[][] graph1, int[][] graph2) {

    // Logic for checking graph isomorphism

    // Replace with your own implementation

    return true;