The name "Shukla graph" is used in this work for the unit-distance graph on 43 vertices and 83 edges constructed by Shukla (2026a, Theorem 1). It has girth 5 and chromatic number 4. This example lowered the known upper bound on the number of vertices needed for a 4-chromatic unit-distance graph of girth 5 from the 45 of the Hochberg-O'Donnell star graph (Hochberg and O'Donnell 1996).
The graph is both 4-vertex-critical and 4-edge-critical. Shukla (2026b) supplies a 3-coloring after every single vertex deletion or edge deletion.
In Shukla's unit-distance embedding, two adjacent vertices are fixed at 
and 
. The remaining 82 coordinates
are the unique real solution in a specified rational box to 82 quadratic
equations, one for each of the other edges. The
resulting points are distinct, and the distance
between two of them is 1 exactly when they represent adjacent vertices
(Shukla 2026a, Lemmas 2 and 3).
