The F26A graph is Hamiltonian.
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. It is also a Cayley graph for the dihedral group D26, generated by a, ab, and ab4, where:
The characteristic polynomial of the F26A graph is equal to
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