널 포인터 에러

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  import java.io.*;
  import java.util.*;
  
  public class Main {
  
      static final int MAX = 100000 + 10;
      static ArrayList<Integer>[] graph;
      static boolean[] visited;
      static int[] answer;
      static int N, M, R;
      static int order;
  
      public static void dfs(int idx) {
          visited[idx] = true;
          answer[idx] = order;
          order++;
  
          for (int i = 0; i < graph[idx].size(); i++) {
              int next = graph[idx].get(i);
              if (!visited[next]) {
                  dfs(next);
              }
          }
  
      }
      public static void main(String[] args) throws IOException {
  
          // 0. 입력 및 초기화
          BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
          BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
  
          StringTokenizer st = new StringTokenizer(br.readLine());
  
          N = Integer.parseInt(st.nextToken());
          M = Integer.parseInt(st.nextToken());
          R = Integer.parseInt(st.nextToken());
  
          graph = new ArrayList[MAX];
          for (int i = 1; i <= N; i++) {
              graph[i] = new ArrayList<>();
          }
          visited = new boolean[MAX];
          answer = new int[MAX];
          order = 1;
  
          for (int i = 0; i < M; i++) {
              st = new StringTokenizer(br.readLine());
              int x = Integer.parseInt(st.nextToken());
              int y = Integer.parseInt(st.nextToken());
              graph[x].add(y);
              graph[y].add(x);
          }
  
          // 2. 내림차순 정렬
          for (int j = 0; j < N; j++) {
              Collections.sort(graph[j], Collections.reverseOrder());
          }
  
          // 3. 재귀함수 출력
          dfs(R);
  
          for (int k = 1; k <= N; k++) {
              bw.write(String.valueOf(answer[k]));
              bw.newLine();
          }
  
          br.close();
          bw.close();
      }
  }

  해당 코드를 구현했는데, 널 포인터 에러가 뜹니다..!
  어떤 부분에서 잘못됐는지 피드백 받고자 질문드립니다!

  
  감사합니다