SOURCE

new Vue({
  el: "#example-5",
  data: {
    selected : 'A',
    seleitems : [
      {text:'red'},
      {text:'blue'},
      {text:'yellow'},
    ]
  }
})

<div id="example-5">
   <select name="" id="" v-model="selected">
     <option v-for="seleitem in seleitems">{{seleitem.text}}</option>
   </select>
  <p>111{{selected}}</p>
  <div v-bind:style={background:selected} class="lgfgf"></div>
</div>

.lgfgf {width: 100px; height: 200px;}