The F26A graph is Hamiltonian and can be described by the LCF notation [−7, 7]13.

[3] It acts transitively on the vertices, on the edges, and on the arcs of the graph.

According to the Foster census, the F26A graph is the only cubic symmetric graph on 26 vertices.

[2] It is also a Cayley graph for the dihedral group D26, generated by a, ab, and ab4, where:[4] The F26A graph is the smallest cubic graph where the automorphism group acts regularly on arcs (that is, on edges considered as having a direction).

[5] The characteristic polynomial of the F26A graph is equal to The F26A graph can be embedded as a chiral regular map in the torus, with 13 hexagonal faces.