King Vegeta's Elite was a group of Saiyan Elites personally led by the king of Planet Vegeta, King Vegeta. The group originally appeared to be a branch within Frieza's forces.
At some point, King Vegeta compromised a group of the most powerful Saiyan Elites/Generals (presumably for the day they would defect from Frieza). During one of their assignments, Prince Vegeta executed several inhabitants of a planet while Nappa and three other Saiyan Elites laughed sadistically. When the inhabitants of the planet defended themselves, the Saiyan Elites shielded themselves (either with technology or their own energy shield). Then, King Vegeta effortlessly destroyed the survivors with an Explosive Wave while Nappa, his son, and the three Elites watched, of which the resulting Explosive Wave was powerful enough to destroy both the planet they were currently on as well as the neighboring planets.
Destruction of the Saiyan race
After a group of Frieza's Elite did away with a band of low-class Saiyans soldiers, King Vegeta and his strongest soldiers staged an invasion of Frieza's spaceship, to which Frieza retaliates by killing King Vegeta and his soldiers. Frieza then obliterates Bardock, Planet Vegeta, and the entire Saiyan race along with it by launching a Supernova through Planet Vegeta.