traverse.js

let arr = [
  {
    id: 1,
    parent: null,
    name: "a"
  },

  {
    id: 2,
    parent: null,
    name: "b"
  },
  {
    id: 3,
    parent: 1,
    name: "c"
  },
  {
    id: 4,
    parent: 1,
    name: "d"
  },
  {
    id: 5,
    parent: 3,
    name: "e"
  },
]

function get_all_children(item) {
  var list = [item.id];
  function node_traverse(rec) {
    for(item of arr) {
      if(rec.id === item.parent) {
        list.push(item.id)
        node_traverse(item)
      }
    }
  }
  node_traverse(item)
  return list;
}

for(item of arr) {
  const children_list = get_all_children(item);
  console.log(children_list);
}