What is the ruling on slaughtering a sheep or camel upon a guest's arrival to visit me at home, as one would welcome kings, if the purpose of this is solely out of custom and tradition?

The Sharia (definition) encourages honoring guests, based on the Prophet's (peace be upon him) saying: "Whoever believes in Allah and the Last Day, let him honor his guest with his prize." And his prize is one day and one night, and hospitality is for three days. It is prescribed to go out of one's way for the guest on the first day, then [serve] whatever is available on the following two days. It is sunnah (definition) to slaughter for the guest, and it is obligatory to preserve any leftover food and not waste it.