So I did some research about how to denote static methods and classes in UML. I found on these two pages that static methods should be denoted by underlining them, but what is the correct way to display a class as being static?
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I would just use a stereotype
<<static>>
Static classes are usually denoted by underlining the class name. Its a convention to underline static features, so it makes sense that underlining the class name would denote a static class.
IMO static classes (like in C#) should not even be used in OO Design. A static class cannot be instantiated and thus is actually not a class regarding UML semantics.
You could mark the class as "leaf" (no subclasses) and add a constraint which does not allow non-static members. This would resemble the meaning of the C# static keyword.
Marking a class as static is a very low level information, which we don't put in UML diagrams usually. UML 1.0 as well as 2.0 gives some flexibility to designer/developer to modify the convention if it suits to your audience/team.
You can put a note to that class, or use something like
<<static>>
( as used for interface).