Leogami

Leogami is the slash ship between Leon Kuwata and Byakuya Togami from the Danganronpa fandom.

Canon
Although the two are never seen interacting in-game or in other material, they both have generally good thoughts about each other. In official Danganronpa relationship charts, all sixteen students give their opinions on one another. In Leon's opinion on Byakuya, he states "The heir of a distinguished family! Cool!" This is notable due to the fact that Leon doesn't tend to hand out compliments to his classmates on a whim. On the other hand, Byakuya's thoughts on Leon read as "He is a difficult being to understand." This would imply that Byakuya is actively attempting to understand Leon, or, at the very least, has attempted to understand him at some point in the past.

In the game, after Leon's execution, Byakuya's expression can be seen in one of his most worried expressions. This comes off as odd, considering his cool nature surrounding the game. Considering that, it is most likely that Byakuya felt sympathetic for the boy, and was shocked to see him so brutally offed.

Fanon
Due to the lack of canon content, the ship is left mostly up to interpretation. Many enjoy the concept of the two of them starting off butting heads, but coming to a resolve at one point or another for various reasons. It is also thought that they would balance each other out in a simple, yet perfect manner. While Leon is a much more go-with-the-flow type of person compared to Byakuya's rather strict mannerisms, they both share traits of competitiveness, drive, and determination. As romantic partners, Leon could teach Byakuya how to open up and become more sympathetic, and Byakuya would more than likely bring out a much more mature side of Leon.

There is also a theory that, had Leon lived longer, he may have confided in Byakuya about the troubles he was having with his talent. In Leon's third Free Time Event, he tells Makoto about his wishes to go back to his old baseball team, meaning that he is at somewhat of an impasse about his career choice. The reason as to why Leon would have gone to Byakuya is simple in most cases: while Leon doesn't know what to do with his life, Byakuya has had his life practically laid out before him, making him the prime candidate to give Leon advice. Due to Byakuya's pride in his work, he most likely would have assisted the other (after a few jabs at Leon's indecisiveness), which would have allowed them to bond.

Leon also showed promising signs of being the one person with enough common sense to try and put an end to Toko's stalkerish behavior towards Byakuya. In the prologue of the game, Leon tells Hifumi off for making an inappropriate comment, meaning that he has a desire to keep everyone comfortable. Toko's obsession begins to grow in Chapter Two, and although she most likely would have been told to keep her inappropriate thoughts to herself by Leon, he is no longer around. The other students, for the rest of the game, let Toko's obsession go practically unchecked; nothing much is done to stop her from making Byakuya uncomfortable, and nothing is done to keep Byakuya from manipulating her. Leon would act as the middle man in this case and ensure that both sides played nicely.