Text this: On the semigroup whose elements are subgraphs of a complete graph

  _____      ___       _____    _____    _    _   
 /  ___||   / _ \\    / ___//  |  ___|| | |  | || 
| // __    | / \ ||   \___ \\  | ||__   | |/\| || 
| \\_\ ||  | \_/ ||   /    //  | ||__   |  /\  || 
 \____//    \___//   /____//   |_____|| |_// \_|| 
  `---`     `---`   `-----`    `-----`  `-`   `-`