If the discs you have are the original install-restore discs with Tiger, they would be gray color and have a series number relating to their use with the iMac model you have.
Is it an iMac 4.1,4.2 5.1, 5.2, 6.1, 7.1 model identifier?
All of these different ones (17"/20"/24") may have shipped
with Tiger OS X 10.4 on original machine series specific DVDs.
Could be the retail disc you have isn't as new as the special iMac installer's Tiger version. Most of this kind of information is documented. Other than the original applications included with the iMac, and the Hardware Test on the original iMac DVD, (plus restoring it before passing it on to some other user) the ability to use the Snow Leopard 10.6 retail DVD, and upgrade that way, is a better direction.
However if you had any older applications and you install Snow Leopard, be sure that retail DVD installs an option contained on the disc, by the name Rosetta; so your older applications that may not have been written for intel-based Macs of that era, could run in Snow Leopard 10.6.8.
Mactracker has a list of all Tiger releases; but under Intel-iMac models
that shipped with Tiger, these are different for specific hardware.
Be sure to have your product model identification number and serial number if you contact Apple for a replacement set of original DVD installer software.
You may be able to get more exact information on what the grey install-restore original DVDs (gray label) are and their identification numbers, in the database at everymac.com. If you can narrow down the model version you have; there was more than one 2006 build, and also the display size can affect the software included.
Good luck & happy computing! 🙂
edited