How to redraw one component?

Question

Vue.js

I use vue-router (I just started learning, I understand what's what).

<div id="app">
    <header_v :authdata="{{ json_encode($url_data) }}"></header_v>
    <router-view></router-view>
</div>

In the header_v component, I have a login variable (whether the user is logged in or not).
router-view - site pages are displayed here depending on the route. So how to make it so that when the value of login changes in the header_v component, then the router-view component is redrawn (updated)?
Or how is this even implemented?
header_v

import axios from 'axios';
    export default {

        props: [
            'authdata'
        ],
        data: function () {
            return {
                login: this.authdata,
                email: '',
                password: ''
            }
        },
        mounted() {
        },
        watch: {},
        methods: {
            exit: function () {
                let t = this;

                axios.post('/api/exit', {
                    _token: $('meta[name="csrf-token"]').attr('content')
                }).then(response => {
                    t.login = null;
                    window.location = '/';
                })
            },
            loginB: function () {
                let t = this;
                axios.post('/api/login', {
                    email: this.email,
                    password: this.password,
                }).then(response => {
                    t.login = response.data;
                    $("#authmodal").modal('hide');
                    t.$router.go();
                })

            },
        }
    }

Answer 1

What does redraw mean? You set the conditions for an authorized and unauthorized user inside and they will work themselves. For example:

<header>
    <div v-if="user">Здравствуйте, {{ user.name }}</div>
    <button v-else>Войти</button>
</header>

user - this is an example, you can substitute anything here, depending on how you distinguish an authorized user from an unauthorized one