methods: {
            initTab: function(){
                document.querySelectorAll('.element').onclick = this.nextTab()
            }
        },
        mounted: function () {
            this.initTab()
        }

<component-name @click="nextTab(tabName)"></component-name>

<ul v-for="tab in tabs">
  <li @click="nextTab(tab)">{{tab}}</li>
</ul>

methods: {
    nextTab: function(tab){
       // whatever it is you want to do here
    }
},