It was named by David Eppstein after the twelve-pointed star in the flag of Nauru.

[3] The Nauru graph requires at least eight crossings in any drawing of it in the plane.

[4][5] The Nauru graph is Hamiltonian and can be described by the LCF notation : [5, −9, 7, −7, 9, −5]4.

[1] The Nauru graph can also be constructed as the generalized Petersen graph G(12, 5) which is formed by the vertices of a dodecagon connected to the vertices of a twelve-point star in which each point of the star is connected to the points five steps away from it.

[6] It is isomorphic to the direct product of the symmetric groups S4 and S3 and acts transitively on the vertices, on the edges and on the arcs of the graph.

[2] The generalized Petersen graph G(n,k) is vertex-transitive if and only if n = 10 and k =2 or if k2 ≡ ±1 (mod n) and is edge-transitive only in the following seven cases: (n,k) = (4,1), (5,2), (8,3), (10,2), (10,3), (12,5), (24,5).

The Nauru graph has two different embeddings as a generalized regular polyhedron: a topological surface partitioned into edges, vertices, and faces in such a way that there is a symmetry taking any flag (an incident triple of a vertex, edge, and face) into any other flag.

The other symmetric embedding of the Nauru graph has six dodecagonal faces, and forms a surface of genus 4.

[9] It and the prisms are the only generalized Petersen graphs G(n,p) that cannot be so represented in such a way that the symmetries of the drawing form a cyclic group of order n. Instead, its unit distance graph representation has the dihedral group Dih6 as its symmetry group.

[11] In 1950, H. S. M. Coxeter cited the graph a second time, giving the Hamiltonian representation used to illustrate this article and describing it as the Levi graph of a projective configuration discovered by Zacharias.

[12][13] In 2003, Ed Pegg wrote in his online MAA column that F24A deserves a name but did not propose one.