Naegami

Naegami is a slash ship between Byakuya Togami and Makoto Naegi in the Dangan Ronpa series.

Canon
''' WARNING: This section contains heavy spoilers for Dangan Ronpa 1 and Dangan Ronpa 3. '''

The first time they meet each other was during the School Life of Mutual Killing, Byakuya saw Makoto under the impression that he was only an ordinary highschooler unworthy of his time. However, as the story progressed, Byakuya began to admire Makoto's investigative skills, although he would never openly voice it. Byakuya often demanded Makoto accompany him on investigations so he could judge whether Makoto would be a threat to him winning the competition. At times he shows little regard for Makoto's well-being, telling him to go die on more than one occasion and volunteering him to open a door after Aoi suggests that the door might explode if they try to open it.

In the second game, Makoto, Byakuya, and Kyouko become companions and he supports Makoto's plan to save the remaining students from the will of the Future Foundation's higher-ups. This new bond is reinforced in Danganronpa 3 when Byakuya is willing to come and rescue them after they were forced to take part in the Final Killing Game. He also gives Makoto a backhanded compliment when they first make contact. Later, he and his men save Makoto from being gunned down brainwashed Future Foundation soldiers.

Fanon
In some Danganronpa fans' opinion it's possible for Byakuya to have a crush on Makoto, however he would never voice it openly because of his personality (just like it was with his admiration for Makoto's investigative skills), while Makoto's docility towards Byakuya was interpreted by them as a concealed liking for him, as he was too shy to confess it to him.