the problem is about shortest path from point x to point y, and DFS dont solve shortest path in graphs ( except for trees ), but Why it don't work ? well, depth first search is about going to the deepest point first , so something like this , , and lets say u want shortest path from 1 to 6 , by using dfs , ur path would be like this 1-2-4-5-3 , it's obvious here , that by Depth first search, the distance from 1 to 5 is 3, while it should 2 ! that was a counter-example on why we shouldn't use depth first search on shortest path problems , but how do we fix it ? well , since we really care about the depth of every node , and when i say depth , i mean the distance from the node i start with , to every node , [for example in previous picture , node 1 was in depth 0 , while node 2,3 was in depth 1 ] then we can use Breadth first search , since we move to every child and go along with it, thus we can easily do the depth of every node accurately , while in depth first search, we were going to the depth of the first child , and when we finish it , we go to the second child and so on .

#include<bits/stdc++.h>
using namespace std;
int BFS(int &start, int &end ,vector<vector<int>>&adj,int &n){
    queue<int>q;
    vector<int>dist(n+2);
    q.push(start);
    dist[start]=0;
    while(!q.empty()){
        int father = q.front();
        q.pop();
        for(auto child : adj[father]){
            if(dist[child] == 0 and child != 1){
                dist[child]= dist[father] + 1;
                q.push(child);
            }
        }
    }
    return dist[end]+1; // because we started with depth 0
}
int main(){
    int n;
    cin>>n;
    int sz = n+3;//make sz equal to the maximum number u can get +1 , example : x,y<=n , then sz =n+1
    vector<vector<int>>adj(sz);//because numbers are up to n
    int start ,end;
    cin>>start>>end;
    for(int i = 0 ; i  <n;i++){
        int x,y;
        cin>>x>>y;
        adj[x].push_back(y);
        adj[y].push_back(x);
    }
    cout<<BFS(start,end,adj,n);

Hope i helped ^^