Authors often name their characters quite deliberately, using names that reflect ideas or themes in the story. Mr. Graves' name is based on the word "grave." If you think about the meaning of the word "grave," you will make the connection with the story. A grave is the place in which we bury a dead person, and the word can also describe someone who is serious and somber, in other words, someone who is not happy and cheerful.
As you read the story carefully, you will see that Mr. Graves is a postmaster, but on the day of the lottery he has some special duties. Those duties result in someone ending up in a grave, and he carries his duties out in a grave way.
Since there are many different versions of "The Lottery," page numbers for quotations will not be very useful to you. I have provided a link to an on-line version of the story, and if you use the "Find on this page" feature, you can find all of the sections of the story in which Mr. Graves is mentioned. Then you can select a few quotes that you like.
Good luck to you.