The
automorphism group of the F26A graph is a group of order 78. It acts transitively on the vertices, on the edges, and on the arcs of the graph. Therefore, the F26A graph is a
symmetric graph (though not
distance transitive). It has automorphisms that take any vertex to any other vertex and any edge to any other edge. According to the
Foster census, the F26A graph is the only cubic symmetric graph on 26 vertices. : D_{26} = \langle a, b | a^2 = b^{13} = 1, aba = b^{-1} \rangle . 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). The
characteristic polynomial of the F26A graph is equal to : (x-3)(x+3)(x^4-5x^2+3)^6. \, ==Other properties==