from typing import Optional
import re


def router_string_is_valid(router_string: Optional[str]) -> bool:
    """
    Validate that the provided router string contains only lowercase alphabetic
    characters and optionally include a hyphen.

    None is a valid option.

    Parameters
    ----------
    router_string: Optional[str]
        The router string to validate.

    Returns
    -------
    status: bool
        The validation status.
    """
    if router_string is None:
        return True

    # Check only lowercase and hyphen allowed
    if re.match(r"^[a-z0-9\-]+$", router_string):
        return True

    return False