Synopsis:
\mathcal{uppercase-letters}
Use a script-like font.
In this example the graph identifier is output in a cursive font.
Let the graph be \( \mathcal{G} \).
If you use something other than an uppercase letter then you do not get an error but you also do not get math calligraphic output. For instance, \mathcal{g} outputs a close curly brace symbol.
© 2007–2018 Karl Berry
Public Domain Software
http://latexref.xyz/Calligraphic.html