Both Junko and Monokuma are members of the Ultimate Despair. Junko appears to be the only student that Monokuma respects, he calls her, "Lady Junko". In Chapter 5, it's revealed that Junko is the one who is controlling Monokuma, as she is the Mastermind of the killing game. Monokuma's personality is heavily based off, on one of Junko's many personalities, that she creates for him.
In Danganronpa Another Episode: Ultra Despair Girls it's shown that Junko was one of the creator's of the Monokuma's. She developed the Monokumas together with Monaca Towa.
MonoJunko is considered as a crack ship in the Danganronpa fandom. Many people in the Danganronpa fandom joke about MonoJunko being Junko's best ship. While the ship isn't meant to be serious since it's a "Human x Robot" ship. Some people draw fan arts of Junko and Monokuma as human and sometimes portray them as couple or as "Partners in Crime". Some also consider the ship to be selfcest, since Junko creates Monokuma's personalities and so, Monokuma and Junko basically have the same personality. Otherwise, both Monokuma and Junko have more popular ship's, such as Junkan and Monokumi.
The ship also sailed, due the Danganronpa fandom's dislike for Junko ship's, since most of them are considered as "toxic" or "abusive", because of Junko's gruesome and mean characters. Some also portray Monokuma, as the child from the ship, Junko x Despair, since Monokuma is a robot bear and was created to spread despair, and Junko loves despair more than anything, so some people came onto the idea that Monokuma is Junko's child. In general, Junko and Monokumas design matches the other one. Junko also wears little Monokuma's in her hair.
Junko and Monokuma are often portrayed together, on Merchandise articles. Like here, Junko Enoshima Strap and here, Junko Rare Figure. Furthermore, Junko and Monokuma are potrayed together on more Merchandise articles, such as this two, were Junko is holding Monokuma in her hand. Junko and Monokuma are also sailed together as Dot Rubber Mascots. Finally, Monokuma is also potrayed on Junko's, Sengoku Asuka Zero x Danganronpa 3 final 6 star card. Monokuma is also portrayed on Junko's Illustration, as he is standing in her pose. Monokuma is also portrayed on one of, Junko's Sprites.