Domain linking to Roadrunner?
 

Possibly the wrong forum, more a computer question, but here goes:

Is it acceptable by the cable comapany to link a domain name to a computer on the roadrunner cable network?

If I understand your question correctly, you seem to be asking whether the cable company (presumably your ISP) would take issue with your setting up a server on their network. Answer is, it depends on your contracted services. If you didn't negotiate an account that permits it, you may find your access disabled. Read the terms of service in your contract.