The council may provide for and regulate the planting of shade and ornamental trees and shrubbery in the streets and public highways of the city and may provide for the care and maintenance thereof. It shall have power to prohibit the maintenance of diseased trees and shrubbery on private premises and if the same will be liable to infect trees and shrubbery on public property or on the property of others, the council may cause entrance upon private premises and destroy such diseased trees and shrubbery, if the owner shall fail to do so after ten (10) days notice served upon him or posted on the premises, and charge the property or the owner thereof in the discretion of the council.