These are chemical agents similar to hormones, but are excreted from the human body and used externally on other creatures of the same species, rather than internally. The thing is that humans have very weak pheromones, if at all, though numerous online retailers will do their best to convince you otherwise.
That said, it's very easy to say that humans can produce a certain type of pheromone which is contained in sweat. So this royal line of yours possesses a dominant gene that grants its descendants the mutation to produce this pheromone, which makes dragons identify them as a friend. Not as a fellow dragon (as this would get your human killed when the adolescent dragons decide to play-wrestle with them), but as some sort of symbiosis.
The real question is how the gene is passed on. If it's on a normal chromosome, than that means that someone who has them on both chromosomes would pass it on to all their children. A hybrid, which would exhibit these symptoms because the gene is dominant, would have a fifty/fifty chance of passing it to any given child.
Or, alternatively, you could make it sex-linked. Linking it to the Y chromosome guarantees that all male offspring down the line would receive it from their father, however it wouldn't be possible for the female to receive it. On the flip side, you could link it to the X, which means a father who had it would pass it on to all his daughters, but none of his sons. If the mother had it, then it'd again be put to a fifty/fifty chance.