a hat
The name of the hat with a flat top worn at graduation ceremonies is called a mortarboard.
grade hat I think the proper name is a Mortar Board
cap and gown. the hat is called a mortarboard.
Mortarboard
in the library
Both are correct and commonly used. "Congratulations on your graduation" and "Congratulations for your graduation" have the same meaning and can be used interchangeably.
Sally's brother's name in The Cat in the Hat is Conrad.
list of post graduation courses
Most commonly it is referred to as a 'morterboard', but often just called a cap.
It was a stovepipe type but I don't think he had a pet name for it although someone will correct me if I'm wrong.
You can get a variety of Sterling Silver and Silver Graduation Necklaces.These have a scroll and the mortarboard hat graduates wear.
Pinterest, Quill and Zazzle are all great companies to check out to gather graduation ideas. It is possible to customize your own graduation hat and order it online as well.