Abstract
Marušič–Scapellato graphs are vertex-transitive graphs of order \(m(2^k + 1)\), where m divides \(2^k - 1\), whose automorphism group contains an imprimitive subgroup that is a quasiprimitive representation of \(\mathrm{SL}(2,2^k)\) of degree \(m(2^k + 1)\). We show that any two Marušič–Scapellato graphs of order pq, where p is a Fermat prime, and q is a prime divisor of \(p - 2\), are isomorphic if and only if they are isomorphic by a natural isomorphism derived from an automorphism of \(\mathrm{SL}(2,2^k)\). This work is a contribution towards the full characterization of vertex-transitive graphs of order a product of two distinct primes.
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Dobson, T. On Isomorphisms of Marušič–Scapellato Graphs. Graphs and Combinatorics 32, 913–921 (2016). https://doi.org/10.1007/s00373-015-1640-4
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DOI: https://doi.org/10.1007/s00373-015-1640-4