The Ukraine SIG (special interest group) page is invaluable.
Most pertinent to Dzygivka is the page on Podolia. This has a listing of articles and other links. Note that Dzygivka is part of Yampol District on the Ukraine SIG map.
The United States Holocaust Memorial Museum has extensive collections. Enter Ukraine in "search". Dzygivka appears only in the oral history or testimony section.
There is an extremely useful and comprehensive section in Wikipedia's History of the Jews in Ukraine.
A Dzygivka Landsmanschaft cemetery in New York. Landsmanschaftn were organizations of immigrants from the same village or town in the "Old Country." They handled many services for immigrants, one of which was burial plots.
YIVO has an extensive collection of records on Landsmanschaftn groups. Unfortunately, the coordinator of this site has not been able to find a Dzygivka listing. It may be embedded in other collections. A personal visit to YIVO may be needed to determine if Dzygivka landsmanschaft records exist and are available.
A Dzygivka cemetery does exist. It was apparently located by Dzygivka researcher Jacqueline Huhem, with the assistance of another researcher, David Cantor, who had the inscribed names translated.
Here is the Huhem-Cantor 2002 report.
The entry gateway appears to say "First Zigiefker Podoler" with the end marking illegible.
The location is Montefiore cemetery. Map.