Maybe so, but Jupiter has been regularly impacted by meteoroids and comets with huge amounts of kinetic energy to little effect. Of course such events pale in comparison to the binding energy of a planet like Earth, which is approx. 60 trillion Gt TNT, which if I've calculated correctly is almost 9 quintillion Tsar Bombas. But if that's the Death Star's normal output, it would need to be 10,000x as powerful to completely blow up Jupiter. Who knows, maybe that's possible if the fusion reaction produced by the Death Star automatically scales up according to the mass of its target. But then I suppose a problem might be that such a large explosion could catch the Death Star itself in its blast radius, shockwave, or lethal particle shower.
Yeah, gravitational energy isn't enough to cause the sort of runaway reaction I'm talking about.
I'm not talking about the target increasing the energy of the Death Star, but whether the energy of the Death Star's weapon can initiate a runaway fusion reaction. Does Yavin simply go up like Alderaan, or does a good chunk of that hydrogen fuse to helium and fry everything around?