Dado el número de vértices en un gráfico de ciclo. La tarea es encontrar el Grado y el número de Bordes del gráfico de ciclo.
Grado: El grado de cualquier vértice se define como el número de aristas que inciden sobre él.
Gráfico de ciclo: en la teoría de gráficos, un gráfico que consta de un solo ciclo se denomina gráfico de ciclo o gráfico circular . El gráfico de ciclo con n vértices se llama Cn .
Propiedades del gráfico de ciclo: –
- Es un grafo conectado.
- Un gráfico de ciclo o gráfico circular es un gráfico que consta de un solo ciclo.
- En un gráfico de ciclo, el número de vértices es igual al número de aristas.
- Un Cycle Graph es coloreable de 2 aristas o de 2 vértices, si y solo si tiene un número par de vértices.
- Un Cycle Graph es coloreable de 3 bordes o coloreable de 3 bordes, si y solo si tiene un número impar de vértices.
- En un gráfico de ciclo, el grado de cada vértice en un gráfico es dos.
- El grado de un gráfico de ciclo es 2 veces el número de vértices. Como cada borde se cuenta dos veces.
Ejemplos:
Input: Number of vertices = 4
Output: Degree is 8
Edges are 4
Explanation:
The total edges are 4
and the Degree of the Graph is 8
as 2 edge incident on each of
the vertices i.e on a, b, c, and d.
Input: number of vertices = 5
Output: Degree is 10
Edges are 5
A continuación se muestra la implementación del problema anterior:
Programa 1: Para gráfico de ciclo de 4 vértices
C++
// C++ implementation of above program.
#include <bits/stdc++.h>
using namespace std;
// function that calculates the
// number of Edge in a cycle graph.
int getnumberOfEdges(int numberOfVertices)
{
int numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
numberOfEdges = numberOfVertices;
// return the numberOfEdges
return numberOfEdges;
}
// function that calculates the degree
int getDegree(int numberOfVertices)
{
int degree;
// The degree of the cycle graph
// will be twice the numberOfVertices
degree = 2 * numberOfVertices;
// return the degree
return degree;
}
// Driver code
int main()
{
// Get the number of vertices
int numberOfVertices = 4;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
cout << "For numberOfVertices = "
<< numberOfVertices
<< "\nDegree = "
<< getDegree(numberOfVertices)
<< "\nNumber of Edges = "
<< getnumberOfEdges(numberOfVertices);
return 0;
}
Java
// Java implementation of above program.
import java.io.*;
class GFG {
// function that calculates the
// number of Edge in a cycle graph.
static int getnumberOfEdges(int numberOfVertices)
{
int numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
numberOfEdges = numberOfVertices;
// return the numberOfEdges
return numberOfEdges;
}
// function that calculates the degree
static int getDegree(int numberOfVertices)
{
int degree;
// The degree of the cycle graph
// will be twice the numberOfVertices
degree = 2 * numberOfVertices;
// return the degree
return degree;
}
// Driver code
public static void main(String[] args)
{
// Get the number of vertices
int numberOfVertices = 4;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
System.out.print("For numberOfVertices = "
+ numberOfVertices
+ "\nDegree = "
+ getDegree(numberOfVertices)
+ "\nNumber of Edges = "
+ getnumberOfEdges(numberOfVertices));
}
}
// This code is contributed by anuj_67..
Python3
# Python3 implementation of above program.
# function that calculates the
# number of Edge in a cycle graph.
def getnumberOfEdges(numberOfVertices) :
# The numberOfEdges of the cycle graph
# will be same as the numberOfVertices
numberOfEdges = numberOfVertices
# return the numberOfEdges
return numberOfEdges
# function that calculates the degree
def getDegree(numberOfVertices) :
# The degree of the cycle graph
# will be twice the numberOfVertices
degree = 2 * numberOfVertices
# return the degree
return degree
# Driver code
if __name__ == "__main__" :
# Get the number of vertices
numberOfVertices = 4
# Find the numberOfEdges and degree
# from the numberOfVertices
# and print the result
print("For numberOfVertices =", numberOfVertices,
"\nDegree =", getDegree(numberOfVertices),
"\nNumber of Edges =", getnumberOfEdges(numberOfVertices))
# This code is contributed by ANKITRAI1
C#
// C# implementation of above program.
using System;
class GFG {
// function that calculates the
// number of Edge in a cycle graph.
static int getnumberOfEdges(int numberOfVertices)
{
int numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
numberOfEdges = numberOfVertices;
// return the numberOfEdges
return numberOfEdges;
}
// function that calculates the degree
static int getDegree(int numberOfVertices)
{
int degree;
// The degree of the cycle graph
// will be twice the numberOfVertices
degree = 2 * numberOfVertices;
// return the degree
return degree;
}
// Driver code
public static void Main()
{
// Get the number of vertices
int numberOfVertices = 4;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
Console.WriteLine("For numberOfVertices = "
+ numberOfVertices
+ "\nDegree = "
+ getDegree(numberOfVertices)
+ "\nNumber of Edges = "
+ getnumberOfEdges(numberOfVertices));
}
}
// This code is contributed by anuj_67..
PHP
<?php
// PHP implementation of above program
// function that calculates the
// number of Edge in a cycle graph.
function getnumberOfEdges($numberOfVertices)
{
$numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
$numberOfEdges = $numberOfVertices;
// return the numberOfEdges
return $numberOfEdges;
}
// function that calculates the degree
function getDegree($numberOfVertices)
{
// The degree of the cycle graph
// will be twice the numberOfVertices
$degree = 2 * $numberOfVertices;
// return the degree
return $degree;
}
// Driver code
// Get the number of vertices
$numberOfVertices = 4;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
echo ("For numberOfVertices = ");
echo ($numberOfVertices);
echo ("\nDegree = ");
echo getDegree($numberOfVertices);
echo("\nNumber of Edges = ");
echo getnumberOfEdges($numberOfVertices);
// This code is contributed by Shivi_Aggarwal
?>
Javascript
<script>
// Javascript implementation of above program.
// function that calculates the
// number of Edge in a cycle graph.
function getnumberOfEdges(numberOfVertices)
{
var numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
numberOfEdges = numberOfVertices;
// return the numberOfEdges
return numberOfEdges;
}
// function that calculates the degree
function getDegree(numberOfVertices)
{
var degree;
// The degree of the cycle graph
// will be twice the numberOfVertices
degree = 2 * numberOfVertices;
// return the degree
return degree;
}
// Driver code
// Get the number of vertices
var numberOfVertices = 4;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
document.write("For numberOfVertices = " +
numberOfVertices + "<br>Degree = " +
getDegree(numberOfVertices) +
"<br>Number of Edges = " +
getnumberOfEdges(numberOfVertices));
// This code is contributed by itsok
</script>
Producción:
For numberOfVertices = 4 Degree = 8 Number of Edges = 4
Programa 2: Para gráfico de ciclo de 6 vértices
C++
// C++ implementation of above program.
#include <bits/stdc++.h>
using namespace std;
// function that calculates the
// number of Edge in a cycle graph.
int getnumberOfEdges(int numberOfVertices)
{
int numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
numberOfEdges = numberOfVertices;
// return the numberOfEdges
return numberOfEdges;
}
// function that calculates the degree
int getDegree(int numberOfVertices)
{
int degree;
// The degree of the cycle graph
// will be twice the numberOfVertices
degree = 2 * numberOfVertices;
// return the degree
return degree;
}
// Driver code
int main()
{
// Get the number of vertices
int numberOfVertices = 6;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
cout << "For numberOfVertices = "
<< numberOfVertices
<< "\nDegree = "
<< getDegree(numberOfVertices)
<< "\nNumber of Edges = "
<< getnumberOfEdges(numberOfVertices);
return 0;
}
Java
// Java implementation of above program.
class GfG {
// function that calculates the
// number of Edge in a cycle graph.
static int getnumberOfEdges(int numberOfVertices)
{
int numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
numberOfEdges = numberOfVertices;
// return the numberOfEdges
return numberOfEdges;
}
// function that calculates the degree
static int getDegree(int numberOfVertices)
{
int degree;
// The degree of the cycle graph
// will be twice the numberOfVertices
degree = 2 * numberOfVertices;
// return the degree
return degree;
}
// Driver code
public static void main(String[] args)
{
// Get the number of vertices
int numberOfVertices = 6;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
System.out.println("For numberOfVertices = "
+ numberOfVertices + "\nDegree = "
+ getDegree(numberOfVertices)
+ "\nNumber of Edges = "
+ getnumberOfEdges(numberOfVertices));
}
}
// This code contributed by Rajput-Ji
Python3
# Python 3 implementation of above program
# function that calculates the
# number of Edge in a cycle graph.
def getnumberOfEdges(numberOfVertices):
numberOfEdges = 0
# The numberOfEdges of the cycle graph
# will be same as the numberOfVertices
numberOfEdges = numberOfVertices
# return the numberOfEdges
return numberOfEdges
# function that calculates the degree
def getDegree(numberOfVertices):
# The degree of the cycle graph
# will be twice the numberOfVertices
degree = 2 * numberOfVertices
# return the degree
return degree
# Driver code
if __name__ == "__main__":
# Get the number of vertices
numberOfVertices = 6
# Find the numberOfEdges and degree
# from the numberOfVertices
# and print the result
print("For numberOfVertices = ",
numberOfVertices, "\nDegree = ",
getDegree(numberOfVertices),
"\nNumber of Edges = ",
getnumberOfEdges(numberOfVertices))
# This code is contributed by ChitraNayal
C#
// C# implementation of above program.
class GfG {
// function that calculates the
// number of Edge in a cycle graph.
static int getnumberOfEdges(int numberOfVertices)
{
int numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
numberOfEdges = numberOfVertices;
// return the numberOfEdges
return numberOfEdges;
}
// function that calculates the degree
static int getDegree(int numberOfVertices)
{
int degree;
// The degree of the cycle graph
// will be twice the numberOfVertices
degree = 2 * numberOfVertices;
// return the degree
return degree;
}
// Driver code
static void Main()
{
// Get the number of vertices
int numberOfVertices = 6;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
System.Console.WriteLine("For numberOfVertices = "
+ numberOfVertices + "\nDegree = "
+ getDegree(numberOfVertices)
+ "\nNumber of Edges = "
+ getnumberOfEdges(numberOfVertices));
}
}
// This code contributed by mits
PHP
<?php
// PHP implementation of above program.
// function that calculates the
// number of Edge in a cycle graph.
function getnumberOfEdges($numberOfVertices)
{
$numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
$numberOfEdges = $numberOfVertices;
// return the numberOfEdges
return $numberOfEdges;
}
// function that calculates the degree
function getDegree($numberOfVertices)
{
$degree = 0;
// The degree of the cycle graph
// will be twice the numberOfVertices
$degree = 2 * $numberOfVertices;
// return the degree
return $degree;
}
// Driver code
// Get the number of vertices
$numberOfVertices = 6;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
echo "For numberOfVertices = " . $numberOfVertices .
"\nDegree = " . getDegree($numberOfVertices) .
"\nNumber of Edges = " .
getnumberOfEdges($numberOfVertices);
// This code is contributed by mits
?>
Javascript
<script>
// Javascript implementation of above program
// function that calculates the
// number of Edge in a cycle graph.
function getnumberOfEdges(numberOfVertices)
{
let numberOfEdges = 0;
// The numberOfEdges of the cycle graph
// will be same as the numberOfVertices
numberOfEdges = numberOfVertices;
// return the numberOfEdges
return numberOfEdges;
}
// function that calculates the degree
function getDegree(numberOfVertices)
{
let degree;
// The degree of the cycle graph
// will be twice the numberOfVertices
degree = 2 * numberOfVertices;
// return the degree
return degree;
}
// Driver code
// Get the number of vertices
let numberOfVertices = 6;
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
document.write("For numberOfVertices = "
+ numberOfVertices + "<br>Degree = "
+ getDegree(numberOfVertices)
+ "<br>Number of Edges = "
+ getnumberOfEdges(numberOfVertices));
// This code is contributed by avanitrachhadiya2155
</script>
Producción:
For numberOfVertices = 6 Degree = 12 Number of Edges = 6
Publicación traducida automáticamente
Artículo escrito por Naman_Garg y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA