Don’t use a regex when you don’t need to 🙂
$valid = filter_var($string, FILTER_VALIDATE_IP);
Though if you really do want a regex…
$valid = preg_match('/^\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}\z/', $string);
The regex however will only validate the format, the max for any octet is the max for an unsigned byte, or 255.
This is why IPv6 is necessary – an IPv4 address is only 32bits long and the internet is popular 🙂