Damocles

He is the father of Tohru and is know as the Emperor of Demise.

Appearance
In his human form, Tohru's father takes a form of a short old man covered with a dark red cloak (black in some occasions), he has long gray hair and a long grey beard, he also has grim-looking eyes.

In his true/dragon form, He is a large dragon, similar to Tohru but with different features, he is a bit bigger than Tohru herself, and bulkier as well, his scales are red with a cream-colored underbelly, he has six horns, two long cream-colored whiskers, red eyes, a long white mane, and sharp wings, his most notable feature being that his overall design is a mix between that of a Japanese dragon, and of a Medieval-European dragon.

Personality
Tohru's father is callous and stern, hating humans and viewing them as inferior and evil - a belief he tried to impart on Tohru. However, unlike other Chaos Dragons, he respects the non-interference laws preventing dragons from killing humans of Earth, although when angered, he attacks Kobayashi and threatens to leave her at the brink of death. Despite this, he cares for his daughter and is concerned for her safety and happiness, warning her that the peaceful human life she claims to want is impossible, and that her presence risks bringing the war of the Chaos and Harmony faction dragons that is ravaging the Other World to Earth.

In the manga, he leaves after Tohru intimidates him, while in the anime, he strongly disapproves of Tohru's choice of mate, but accepts her decision and leaves her in peace.

Plot Manga
Tohru's father shows up on Kobayashi's doorstep to demand Tohru's return home to the Other World. When Tohru refuses, he explains to her that the peaceful human life she desires is impossible, and that sooner or later she will be found out or would lose control of her bloodlust, and that even if that does not happen Kobayashi's lifespan is miniscule compared to hers. Further repremanding her for breaking the non-interference laws, he warns her that her presence risks drawing other dragons to Earth. When Kobayashi mocks him, he attacks her but is stopped by Tohru, who intimidates him into leaving.

Plot Anime
He approaches Tohru while his daughter is struggling with the realization of Kobayashi's relatively short lifespan. The Emperor of Demise returns Tohru to the Other World, and when she returns several days later, he confronts her over her defiance. When Kobayashi tries to interrupt their argument, he destroys her glasses and threatens to leave her on the brink of death unless she chooses her words carefully. When Kobayashi's speech restores Tohru's resolve, the Emperor of Demise challenges her to a battle, opening a portal to an isolated area. Their fight is interrupted by Kobayashi and Kanna, who urges them to reach a compromise. While he refuses to approve of Tohru's choice of mate, the Emperor of Demise decides to respect her decisions and returns to the Other World.

Tohru
Though he is very caring of his daughter, he was immediately appalled and angered upon seeing her daughter defect to the other world and affiliating herself with a human. At one point, he took Tohru back into her world, only for her to come back to the other world and confront her and Kobayashi at her defiance. Eventually, this confrontation even escalated into a full-on battle, showing that he is willing to use force if he feels that it is for her own good. After Kobayashi confronts him, he calls his offspring foolish, but it would appear that this was not so much meant as an insult, or a statement expressing a genuine lack of faith in her intelligence, but a statement comparable to when one calls their children their "silly little _," and more affectionate that chastising. Past the ruthlessness, cold-bloodedness, prejudice, and at times downright meanness, he seems to genuinly want his daughter to be happy and safe.

Kobayashi
At first, it seems as if he may in fact almost completely disregard Kobayashi's existence, seeing her not as a person but a fanciful notion his daughter has, in his opinion, foolishly chosen to pursue, although in Tohru's flashbacks he is known to have expressed the belief that all humans are evil and should be killed when possible. However, when she stands up for Tohru, he is quick to show his lack of good-will, willing to let her live as is law, but attacking the moment she tries to speak and threatening her with near-death should he so much as choose her words wrong. This is likely a result of both his general disposition against humans and that he see's her as a threat to his daughter's well-being. He appears honestly incapable of believing that a human could care about a dragon, though he agrees with her when she comments on how "awesome" Tohru is. However once Kobayashi demands he back off and that his daughter was hers, he expressed that she has overstepped a human's place. Later, when Kobayashi arrives to interrupts the battle, he initially expresses that human has no place in dragons' affairs, that they could never understand them, and that coexistence is impossible. However, her passion and talk of respect surprise him, and it would seem that he is finally moved when she tells him to "try having some faith in [his] daughter!" In the end, he takes his leave, and it would seem that, though he does not approve of the human, as he feels that her short lifespan will only break Tohru's heart (and therefore that she's not worth his daughter's time), he would appear to have secretly begun to respect her, if only a bit.

Powers and Abilities
He is, arguably, the strongest dragon in the series so far, far exceeding Tohru and even Fafnir in terms of strength and magic power, not even flinching after taking hits from Tohru. He eradicates a vase nearby Kobayashi in the manga (in the anime, her glasses are snapped in half instead). He would appear to breathe some sort of purple fire.

Trivia

 * It wasn't clarified yet whether "Emperor of Demise" is an actual royal title he holds or just an epithet about his great power and his high position in the Chaos faction.