Check whether given degrees of vertices represent a Graph or Tree

Difficulty Level : Basic
Last Updated : 07 Feb, 2019

Given the number of vertices and the degree of each vertex where vertex numbers are 1, 2, 3,…n. The task is to identify whether it is a graph or a tree. It may be assumed that the graph is connected.

Examples:

Input : 5
        2 3 1 1 1
Output : Tree
Explanation : The input array indicates that 
              vertex one has degree 2, vertex
              two has degree 3, vertices 3, 4 
              and 5 have degree 1.  
            1
           / \
          2   3
         / \
        4   5


Input : 3
        2 2 2
Output : Graph      
            1
           / \
          2 - 3

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The degree of a vertex is given by the number of edges incident or leaving from it.
This can simply be done using the properties of trees like –

Tree is connected and has no cycles while graphs can have cycles.
Tree has exactly n-1 edges while there is no such constraint for graph.
It is given that the input graph is connected. We need at least n-1 edges to connect n nodes.

If we take the sum of all the degrees, each edge will be counted twice. Hence, for a tree with n vertices and n – 1 edges, sum of all degrees should be 2 * (n – 1). Please refer Handshaking Lemma for details.

So basically we need to check if sum of all degrees is 2*(n-1) ore not.

C++

// C++ program to check whether input degree
// sequence is graph or tree
#include<bits/stdc++.h>
using namespace std;
  
// Function returns true for tree
// false for graph
bool check(int degree[], int n)
{
    // Find sum of all degrees
    int deg_sum = 0;
    for (int i = 0; i < n; i++)
        deg_sum += degree[i];
  
    // Graph is tree if sum is equal to 2(n-1)
    return (2*(n-1) == deg_sum);
}
  
// Driver program to test above function
int main()
{
    int n = 5;
    int degree[] = {2, 3, 1, 1, 1};
  
    if (check(degree, n))
        cout << "Tree";
    else
        cout << "Graph";
  
    return 0;
}

Java

// Java program to check whether input degree 
// sequence is graph or tree 
class GFG 
{
  
    // Function returns true for tree 
    // false for graph 
    static boolean check(int degree[], int n)
    {
        // Find sum of all degrees 
        int deg_sum = 0;
        for (int i = 0; i < n; i++) 
        {
            deg_sum += degree[i];
        }
  
        // Graph is tree if sum is equal to 2(n-1) 
        return (2 * (n - 1) == deg_sum);
    }
  
    // Driver code 
    public static void main(String[] args)
    {
        int n = 5;
        int degree[] = {2, 3, 1, 1, 1};
  
        if (check(degree, n))
        {
            System.out.println("Tree");
        } 
        else 
        {
            System.out.println("Graph");
        }
    }
} 
  
  
// This code has been contributed 
// by 29AjayKumar

Python

# Python program to check whether input degree
# sequence is graph or tree
def check(degree, n):
      
    # Find sum of all degrees
    deg_sum = sum(degree)
      
    # It is tree if sum is equal to 2(n-1)
    if (2*(n-1) == deg_sum):
        return True
    else:
        return False
      
#main
n = 5
degree = [2, 3, 1, 1, 1];
if (check(degree, n)):
    print "Tree"
else:
    print "Graph"

C#

// C# program to check whether input 
// degree sequence is graph or tree 
using System;
  
class GFG 
{
  
    // Function returns true for tree 
    // false for graph 
    static bool check(int[] degree, int n)
    {
        // Find sum of all degrees 
        int deg_sum = 0;
        for (int i = 0; i < n; i++) 
        {
            deg_sum += degree[i];
        }
  
        // Graph is tree if sum is 
        // equal to 2(n-1) 
        return (2 * (n - 1) == deg_sum);
    }
  
    // Driver code 
    public static void Main()
    {
        int n = 5;
        int[] degree = {2, 3, 1, 1, 1};
  
        if (check(degree, n))
        {
            Console.WriteLine("Tree");
        } 
        else
        {
            Console.WriteLine("Graph");
        }
    }
} 
  
// This code has been contributed 
// by Akanksha Rai

PHP

<?php
// PHP program to check whether input 
// degree sequence is graph or tree
  
// Function returns true for tree
// false for graph
function check(&$degree, $n)
{
    // Find sum of all degrees
    $deg_sum = 0;
    for ($i = 0; $i < $n; $i++)
        $deg_sum += $degree[$i];
  
    // Graph is tree if sum is 
    // equal to 2(n-1)
    return (2 * ($n - 1) == $deg_sum);
}
  
// Driver Code
$n = 5;
$degree = array(2, 3, 1, 1, 1);
  
if (check($degree, $n))
    echo "Tree";
else
    echo "Graph";
  
// This code is contributed by 
// Shivi_Aggarwal
?>

Output:

Tree

This article is contributed by Ayush Khanduri. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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