Abstract
A graph is symmetric (or arc-transitive) if its automorphism group is transitive on the arc set of the graph. Let r<q<p be three distinct primes. In this paper, we give a complete classification of connected pentavalent symmetric graphs of order 2pqr with r≥3. It is shown that a connected pentavalent symmetric graph Γ of order 2pqr is isomorphic to one of 20 sporadic coset graphs associated with some simple groups, a coset graph on the group PSL(2,p) or PGL(2,p) with p≥29 and Aut(Γ)≅PSL(2,p) or PGL(2,p) respectively, or a 1-regular graph given in Feng and Li (2011). The connected pentavalent symmetric graphs of order 4pq have been classified before.
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