How to validate Fully Qualified Domain with bash script?

#!/bin/bash

fqdn="www.google.com"

#FQDN Validation
{
        echo $fqdn | grep -P "^(([a-zA-Z0-9]|[a-zA-Z0-9][a-zA-Z0-9\-]*[a-zA-Z0-9])\.)*([A-Za-z0-9]|[A-Za-z0-9][A-Za-z0-9\-]*[A-Za-z0-9])$"
} && {
        echo "valid FQDN"  
} || {
        echo "Invalid FQDN Address"
exit 1
}