널 포인터 에러

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