On Isomorphisms of Marušič–Scapellato Graphs
| Autor: | Ted Dobson |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Degree (graph theory) 0102 computer and information sciences Automorphism 01 natural sciences Theoretical Computer Science Combinatorics Vertex-transitive graph 010201 computation theory & mathematics Prime factor Discrete Mathematics and Combinatorics Order (group theory) Isomorphism Graph isomorphism Graph automorphism Mathematics |
| Zdroj: | Graphs and Combinatorics. 32:913-921 |
| ISSN: | 1435-5914 0911-0119 |
| DOI: | 10.1007/s00373-015-1640-4 |
| Popis: | Marusia?---Scapellato graphs are vertex-transitive graphs of order $$m(2^k + 1)$$m(2k+1), where m divides $$2^k - 1$$2k-1, whose automorphism group contains an imprimitive subgroup that is a quasiprimitive representation of $$\mathrm{SL}(2,2^k)$$SL(2,2k) of degree $$m(2^k + 1)$$m(2k+1). We show that any two Marusia?---Scapellato graphs of order pq, where p is a Fermat prime, and q is a prime divisor of $$p - 2$$p-2, are isomorphic if and only if they are isomorphic by a natural isomorphism derived from an automorphism of $$\mathrm{SL}(2,2^k)$$SL(2,2k). This work is a contribution towards the full characterization of vertex-transitive graphs of order a product of two distinct primes. |
| Databáze: | OpenAIRE |
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