Sans & Gaster: coworkers. I think of them as employed to each other.

Gaster/Gerson: Their relationship was THE first thing to die when monsters got sealed underground. Would have been a friendgroup destroying breakup if asgore & toriel didn't refuse to take sides.

Asgore/Toriel: Divorced so bad.. zero salvaging. If they didn't love each other as much as they did before it all went wrong, it wouldn't be so bad. But alas.

Asgore/Toriel/Gaster: There was an attempt. Gaster didn't get the hint, so asgoriel stopped flirting.

Asgore/Toriel/Gerson: Less of an attempt. More casual than direct, if the plan hadn't happened, maybe there would have been something.

Asgore/Gerson: Gerson wins by doing nothing! Old friends for hundreds of hundreds of years that may or may not have 'raised' a kid together. Roommates post-pacifist. Not ever going to be something with a label.

Asgore/Rudy: Missed opportunity. Asgore never even realized he had feelings, and by the time he did, it was far too late.

Asgore & Carol: Close friends. Carol recognizes Asgores' feelings for her deceased husband even if he never tells her. Not really threatened so much as she wouldn't have minded sharing. They reminisce over tea.

Carol/Rudy: lovingly married. Carol is a widow now.

Carol/Toriel: Friends, Carol is the head of the brand new PTA for Toriels school, so they spend a lot of time together. They butt heads more often than not but have split many bottles of wine together on late nights...

Grillby/Gaster: ex friends with benefits and just ex friends in general. Gasters' growing obsession with the dark led him to push grillby away...

Grillby/sans: joker and joke hostage. Sans picks up shifts when needed and, when not needed, is forcing grillby into his own personal test audience. Grillby appreciates the help, but if he has to hear another fire pun...

Grillby/Toriel: sans introduced them, grillby used to have a crush on the idea of the queen back when he was in the royal guard, and now? She's here?? Calling him hotstuff?? Mortifying for him, she's just happy to have a new friend (and has so many fire puns prepared)

Toriel/Sans: joke accomplices... he takes the job of introducing her around post-pacifist. They both really enjoy each others company, and when not busy, they are usually hanging around each other. unlikely to ever get a 'real' lable, but do they NEED one?

-not on the chart but I had thoughts about them so-

Gerson/Grillby: My war yaoi... met a few times over the course of the war and not much after, Grillby was a new recruit and admired Gerson as the 'hammer of justice'. Gerson comes to drink at his bar a few times but always calls Grillby 'kid'. Another old one-sided crush on grillbys part

Carol & sans: Met once. Did not like each other.