Skip to content
Related Articles

Related Articles

Program to find the diameter, cycles and edges of a Wheel Graph

Improve Article
Save Article
  • Last Updated : 05 Sep, 2022
Improve Article
Save Article

Wheel Graph: A Wheel graph is a graph formed by connecting a single universal vertex to all vertices of a cycle. 

Properties:

  • Wheel graphs are Planar graphs.
  • There is always a Hamiltonian cycle in the Wheel graph.
  • Chromatic Number is 3 and 4, if n is odd and even respectively.

Problem Statement: 

Given the Number of Vertices in a Wheel Graph. The task is to find:

  1. The Number of Cycles in the Wheel Graph.
  2. A number of edges in Wheel Graph.
  3. The diameter of a Wheel Graph.

Examples:

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

Example #1: For vertices = 4 Wheel Graph, total cycle is 7

 Example #2:  For vertices = 5 and 7 Wheel Graph Number of edges = 8 and 12 respectively: 

 Example #3: For vertices = 4, the Diameter is 1 as We can go from any vertices to any vertices by covering only 1 edge. 

 Formula to calculate the cycles, edges and diameter:

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

Below is the required implementation: 

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
?>

Output

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

My Personal Notes arrow_drop_up
Related Articles

Start Your Coding Journey Now!