is_graph_a_tree.py

from os import *
from sys import *
from collections import *
from math import *

def checkgraph(edges, n, m):
    neighbors = defaultdict(set) 
    for node1, node2 in edges:
        neighbors[node1].add(node2)
        neighbors[node2].add(node1)
    
    def dfs(root, visited):  
        if root in visited:
            return False
        visited.add(root)

        for neighbor in neighbors[root]:
            neighbors[neighbor].remove(root)
            if not dfs(neighbor, visited):
                return False

        return True

    visited = set() 
    result = dfs(edges[0][0], visited) and len(visited) == n
    return result