Check whether given degrees of vertices represent a Graph or Tree - GeeksforGeeks

18 Apr, 2022
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
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.
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) or not. 
C++
Java
Python
C#
PHP
// 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 graphbool 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 functionint main(){    int n = 5;    int degree[] = {2, 3, 1, 1, 1};     if (check(degree, n))        cout << "Tree";    else        cout << "Graph";     return 0;}
// Java program to check whether input degree// sequence is graph or treeclass 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 program to check whether input degree# sequence is graph or treedef 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     #mainn = 5degree = [2, 3, 1, 1, 1];if (check(degree, n)):    print "Tree"else:    print "Graph"
// C# program to check whether input// degree sequence is graph or treeusing 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 program to check whether input// degree sequence is graph or tree // Function returns true for tree// false for graphfunction 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 write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
29AjayKumar
Shivi_Aggarwal
Akanksha_Rai
surinderdawra388
Graph
Graph
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Best First Search (Informed Search)
Graph Coloring | Set 2 (Greedy Algorithm)
Maximum Bipartite Matching
Graph Coloring | Set 1 (Introduction and Applications)
Longest Path in a Directed Acyclic Graph
Find minimum s-t cut in a flow network
Find if there is a path between two vertices in a directed graph
Implementation of Graph in JavaScript
Eulerian path and circuit for undirected graph
Iterative Deepening Search(IDS) or Iterative Deepening Depth First Search(IDDFS)