(a) A grandparent of a minor child may petition the court for reasonable rights of visitation of a minor child when one or more of the following circumstances exists:
(1) The parents of the minor child are currently living separately and apart on a permanent or indefinite basis.
(2) One of the parents has been absent for not less than one month, without the other parent's knowing the whereabouts of the absent parent.
(3) The child is not residing with either parent and has not been legally adopted.
(4) The child's parent, who is the child of the grandparents, has died and the parent has not married a spouse who has legally adopted the child.
(b) The petitioner shall give notice of the petition by personal service, pursuant to the Rules of the Superior Court, to each of the parents of the child, any stepparent, and any person who has physical custody of the child.