If you are the owner of a building or property in Virginia that allows public access, and do not wish firearms to be allowed on the premises, you must comply to Virginia's gun sign laws pursuant to § 18.2-308.01 .
Va. Code Ann. § 18.2-308.01. Carrying a concealed handgun with a permit. C. The granting of a concealed handgun permit pursuant to this article shall not thereby authorize the possession of any handgun or other weapon on property or in places where such possession is otherwise prohibited by law or is prohibited by the owner of private property.