input: import re
  
  def is_numeric_string(string: str) -> bool:
      """ Check if the given string is a valid numeric string by using a regular expression.
      >>> is_numeric_string('123456789')
      True
      >>> is_numeric_string('abc123')
      False
      >>> is_numeric_string('123.456')
      False
      """
      pattern = '^[0-9]+$'
      result = re.match(pattern, string)
      return bool(result)
output:     return bool(result)