This popular vote for United States Senator was technically only an advisory vote as prior to the adoption of the 17th Amendment in 1913, state legislatures officially elected United States Senators. The Nevada Legislature ratified King's election on January 25, 1911.
The primary source is the official manuscript returns in the 1898-1918 poll book, located at the Nevada State Archives in Carson City. The returns were also printed in 1909-1910 Biennial Report of the Secretary of State.
George Nixon would die in office on June 5, 1912. The governor appointed William A. Massey to fill the vacancy, pending a special election in 1912, which Massey subsequently lost to Key Pittman (both in the popular vote and legislature vote).
Source for Popular Vote data: Nevada State Archives, "Choice for United States Senator," Election Returns of General Election held on the 8th day of November A.D. 1910 (Carson City, 1910)