My ASP.Net MVC5 application allows users to create their own trip database using google maps api. Now I would like to allow them to post on their facebook walls those trips. Do
I guess you could use OpenGraph Custom Stories to achieve that. Have a look at the guide at https://developers.facebook.com/docs/opengraph/getting-started to get an overview.
Baseline is that you could post via OpenGraph Actions/Stories something like "User XYZ created a Trip with MapMyTrips" to the authenticated User's activities, and when Users click on it they get referred to your site and the individual Trip.