Programa para hallar el diámetro, ciclos y aristas de una Rueda Gráfica

Gráfico de rueda: un gráfico de rueda es un gráfico formado al conectar un solo vértice universal a todos los vértices de un ciclo. Propiedades:-

• Los gráficos de ruedas son gráficos planos.
• Siempre hay un ciclo hamiltoniano en el gráfico de rueda.
• Número cromático es 3 y 4, si n es par e impar respectivamente.

Declaración del problema: dado el número de vértices en un gráfico de rueda. La tarea es encontrar:

1. El número de ciclos en el gráfico de la rueda.
2. Número de aristas en Wheel Graph.
3. El diámetro de un gráfico de rueda.

Ejemplos:

Input: vertices = 4
Output: Number of cycle = 7
         Number of edge = 6
         Diameter = 1

Input: vertices = 6
Output: Number of cycle = 21
         Number of edge = 10
         Diameter = 2

Ejemplo #1: Para vértices = Gráfico de 4 ruedas, el ciclo total es 7 :


Ejemplo #2: Para vértices = 5 y 7 Rueda Gráfico Número de aristas = 8 y 12 respectivamente:


Ejemplo #3: Para vértices = 4, el Diámetro es 1 ya que podemos pasar de cualquier vértice a cualquier vértice cubriendo solo 1 borde.



Fórmula para calcular los ciclos, aristas y diámetro:-

Number of Cycle = (vertices * vertices) - (3 * vertices) + 3
Number of edge = 2 * (vertices - 1)
Diameter = if vertices = 4, Diameter = 1
           if vertices > 4, Diameter = 2

A continuación se muestra la implementación requerida:

C++

// C++ Program to find the diameter,  // cycles and edges of a Wheel Graph #include <bits/stdc++.h> using namespace std;    // Function that calculates the // Number of Cycle in Wheel Graph. int totalCycle(int vertices) {     int result = 0;        // calculates no. of Cycle.     result = pow(vertices, 2) - (3 * vertices) + 3;        return result; }    // Function that calculates the // Number of Edges in Wheel graph. int Edges(int vertices) {     int result = 0;        result = 2 * (vertices - 1);        return result; }    // Function that calculates the // Diameter in Wheel Graph. int Diameter(int vertices) {     int result = 0;        // calculates Diameter.     if (vertices == 4)         result = 1;     else         result = 2;        return result; }    // Driver Code int main() {     int vertices = 4;        cout << "Number of Cycle = " << totalCycle(vertices) << endl;     cout << "Number of Edges = " << Edges(vertices) << endl;     cout << "Diameter = " << Diameter(vertices);        return 0; }

Java

//Java Program to find the diameter,  // cycles and edges of a Wheel Graph import java.io.*;    class GFG {     // Function that calculates the      // Number of Cycle in Wheel Graph.      static int totalCycle(double vertices)      {          double result = 0;         int result1 = 0;                  // calculates no. of Cycle.          result = Math.pow(vertices, 2) - (3 * vertices) + 3;                   result1 = (int)(result);         return result1;      }               // Function that calculates the      // Number of Edges in Wheel graph.      static int Edges(int vertices)      {          int result = 0;                   result = 2 * (vertices - 1);                   return result;      }               // Function that calculates the      // Diameter in Wheel Graph.      static int Diameter(int vertices)      {          int result = 0;                   // calculates Diameter.          if (vertices == 4)              result = 1;          else             result = 2;                   return result;      }            //Driver Code     public static void main(String[] args)     {         int vertices = 4;                    System.out.println("Number of Cycle = " + totalCycle(vertices));         System.out.println("Number of Edges = " + Edges(vertices));         System.out.println("Diameter = " + Diameter(vertices));     } }

Python3

# Python3 Program to find the diameter,  # cycles and edges of a Wheel Graph     # Function that calculates the  # Number of Cycle in Wheel Graph.  def totalCycle(vertices):         result = 0        # calculates no. of Cycle.      result = (pow(vertices, 2) -               (3 * vertices) + 3)     return result     # Function that calculates the  # Number of Edges in Wheel graph.  def Edges(vertices):         result = 0     result = 2 * (vertices - 1)      return result     # Function that calculates the  # Diameter in Wheel Graph.  def Diameter(vertices):         result = 0        # calculates Diameter.      if vertices == 4:          result = 1     else:         result = 2        return result     # Driver Code  if __name__ == "__main__":        vertices = 4        print("Number of Cycle =",             totalCycle(vertices))      print("Number of Edges =", Edges(vertices))      print("Diameter =", Diameter(vertices))     # This code is contributed by Rituraj Jain

C#

// C# Program to find the diameter,  // cycles and edges of a Wheel Graph using System; class GFG { // Function that calculates the  // Number of Cycle in Wheel Graph.  static int totalCycle(double vertices)  {      double result = 0;     int result1 = 0;        // calculates no. of Cycle.      result = Math.Pow(vertices, 2) -                      (3 * vertices) + 3;         result1 = (int)(result);     return result1;  }     // Function that calculates the  // Number of Edges in Wheel graph.  static int Edges(int vertices)  {      int result = 0;         result = 2 * (vertices - 1);         return result;  }     // Function that calculates the  // Diameter in Wheel Graph.  static int Diameter(int vertices)  {      int result = 0;         // calculates Diameter.      if (vertices == 4)          result = 1;      else         result = 2;         return result;  }    // Driver Code public static void Main() {     int vertices = 4;            Console.WriteLine("Number of Cycle = " +                        totalCycle(vertices));     Console.WriteLine("Number of Edges = " +                             Edges(vertices));     Console.WriteLine("Diameter = " +                         Diameter(vertices)); } }    // This code is contributed by inder_verma

PHP

<?php // PHP Program to find the diameter,  // cycles and edges of a Wheel Graph    // Function that calculates the // Number of Cycle in Wheel Graph. function totalCycle($vertices) {     $result = 0;        // calculates no. of Cycle.     $result = pow($vertices, 2) -                   (3 * $vertices) + 3;        return $result; }    // Function that calculates the // Number of Edges in Wheel graph. function Edges($vertices) {     $result = 0;        $result = 2 * ($vertices - 1);        return $result; }    // Function that calculates the // Diameter in Wheel Graph. function Diameter($vertices) {     $result = 0;        // calculates Diameter.     if ($vertices == 4)         $result = 1;     else         $result = 2;        return $result; }    // Driver Code $vertices = 4;    echo "Number of Cycle = " ,        totalCycle($vertices), "\n"; echo "Number of Edges = " ,        Edges($vertices), "\n" ; echo "Diameter = " , Diameter($vertices);    // This code is contributed by inder_verma ?>

Producción:

Number of Cycle = 7
Number of Edges = 6
Diameter = 1