Iofinova and Ivanov proved in 1985 the existence of five and only five semi-symmetric cubic bipartite graphs whose automorphism groups act primitively on each partition.

The diameter of the 110-vertex Iofinova–Ivanov graph, the greatest distance between any pair of vertices, is 7.

It is 3-connected and 3-edge-connected: to make it disconnected at least three edges, or at least three vertices, must be removed.

The chromatic number of the 110-vertex Iofina-Ivanov graph is 2: its vertices can be 2-colored so that no two vertices of the same color are joined by an edge.

Its chromatic index is 3: its edges can be 3-colored so that no two edges of the same color met at a vertex.

The characteristic polynomial of the 110-vertex Iofina-Ivanov graph is

The symmetry group of the 110-vertex Iofina-Ivanov is the projective linear group PGL2(11), with 1320 elements.

[4][5] It is only for the five Iofina-Ivanov graphs that the symmetry group acts primitively on each partition of the vertices.