How to use routing in vue js?

Question

I am working on a vue js project, to use the router , I installed via command -> npm install vue-router and created a router.js file , but when i try , npm run serve, i get compile warnings and the app doesn't work as intended.

Error

warning in ./src/router.js

export 'default' (imported as 'Router') was not found in 'vue-router' ( possible exports: NavigationFailureType, RouterLink ....)

Directory Structure

vuejsproj
  > node_modules
  > public
  > src
      > assets
      > components 
      App.vue
      main.js
      router.js
    ...

router.js

import Vue from "vue";
import Router from "vue-router";
Vue.use(Router);
export default new Router({
  mode: "history",
  routes: [
    {
      path: "/",
      alias: "/list",
      name: "list",
      component: () => import("./components/somecomponent")
    }
  ]
});

main.js

import Vue from 'vue'
import App from './App.vue'
import vuetify from './plugins/vuetify'
import router from './router'
Vue.config.productionTip = false
new Vue({
  router,
  vuetify,
  render: h => h(App)
}).$mount('#app')

package.json

{
  "name": "app",
  "version": "0.1.0",
  "private": true,
  "scripts":{
    "serve": "vue-cli-service serve",
    "build": "vue-cli-service build",
    "lint": "vue-cli-service lint"
  },
  "dependencies": {
    "axios": "^0.27.2",
    "core-js": "^3.8.3",
    "vue": "^2.6.14",
    "vue-axios": "^3.4.1",
    "vue-router": "^4.015",
    "vuetify": "^2.6.0"
  },
  
}