<XML><RECORDS><RECORD><REFERENCE_TYPE>0</REFERENCE_TYPE><REFNUM>5902</REFNUM><AUTHORS><AUTHOR>Miller,A.</AUTHOR><AUTHOR>Praeger,C.</AUTHOR></AUTHORS><YEAR>1994</YEAR><TITLE>Non-Cayley vertex-transitive graphs of order twice the product of two odd primes</TITLE><PLACE_PUBLISHED> Journal of Algebraic combinatorics 3 </PLACE_PUBLISHED><PUBLISHER>Kluwer</PUBLISHER><PAGES>77--111</PAGES><LABEL>Miller:1994:5902</LABEL><ABSTRACT>For a positive interger n, does there exist a vertex-transitive graph Gamma on n vertices which is not a Cayley graph, or, equivalently, a graph Gamma on n vertices such that Aut Gamma is transitive on vertices but none of its subgroups are regular on vertices? In this paper we consider the simplest unresolved case for even integers, namely for integers of the form n=2pq, where 2<q<p and p and q are primes. </ABSTRACT></RECORD></RECORDS></XML>