Is there any way to trigger component method from parent in VueJS?

Yup, just find your component in children array, or grab it by ref attribute, and call method :) ref doc

lets assume that your child component has method x. According to documentation:

<div id="parent">
  <user-profile ref="profile"></user-profile>
</div>

var child = this.$refs.profile;
child.x();

I think a good pattern for this is emitting an event from the parent component and listening to it in the child component, using an Event Bus.

That would be:

in main.js

export const bus = new Vue()

in Parent.vue:

import {bus} from 'path/to/main'

// Where you wanna call the child's method:
bus.$emit('customEventName', optionalParameter)

in Child.vue:

import {bus} from 'path/to/main'

// Add this to the mounted() method in your component options object:
bus.$on('customEventName', this.methodYouWannaCall)