Tessellation with Starfire Protocol is kind of cool.
For starters, let it be known that I do not play Vanguard alerts or raids very often, but I thought this build might be cool. (Mid gameplay I know)
So here is the build: Starfire Protocol + Fusion Grenade (you get 2 of them, and they get recharged with Starfire when radiant) + Tessellation built-in Demolitionist. Whenever you get kills, either on the alt-fire mode or regular fusion mode = many grenades.
One thing about Tessellation: the rocket mode not only deals a ton of damage on its own, with the catalyst, it also inflicts 70 Scorch stacks (which count for the recharge of grenades). Combined with Ember of Ashes, it's pretty much a guaranteed ignition (which also helps).
What we need to do is get as much radiant uptime as we can. How? Two ways, actually:
Firstly, on solar subclass: Fragment Ember of Torches. Hit melee, you get radiant — easy as that.
Second, Hunter's Journal: Radiant Orbs. Pick up an orb, we get radiant.
Plus, if we use Ember of Empyrean to extend solar buffs with solar kills, and Ember of Solace = lots of radiant uptime.
But now we need melee energy. How?
Heat Rises: kills while airborne grant chunks of melee energy. I recommend Phoenix Dive for Resto since it's mainly a weapons-and-buffs build.
I use Icarus Dash as a second aspect for extra fragments. Besides what's above, you can use whatever you want.
As for stats: get Weapons as high as possible, then focus on melee, and then grenade.