On the top of the Luger just in front of the action before the barrel starts is a four digit number In this case 1918 is this the serial number?

No, the 1918 is the date of manufacture of that particular gun. The serial number has more digits, likely five or six. If yours is a "matching Luger" then that means that the gun still has all of the original parts. You can tell this by looking for a two digit number on almost all of the smaller parts (toggle, barrel, barrel extension, trigger, trigger plate, bolt, etc). This number should be the same on all the parts and is the last two digits of the main serial number that is on the frame somewhere. If it is a completely matching Luger, then the magazine number will also match. Most of them don't, however.

Most military lugers have between 2 and 4 numbers for the serial.

some commercial lugers have up to five number serial.