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{\bf Ljiljana Brankovi\' c,  Mirka Miller, J\'an Plesn\'{\i}k, 
Joe Ryan and Jozef \v Sir\'a\v n}
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{\bf A Note on Constructing Large Cayley Graphs of
        Given Degree and Diameter by Voltage Assignments }
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Voltage graphs are a powerful tool for constructing large graphs
(called {\it lifts}) with prescribed properties as covering spaces of
small {\it base} graphs. This makes them suitable for application to
the {\it degree/diameter problem}, which is to determine the largest
order of a graph  with given degree and diameter.

Many currently known largest graphs of degree $\le 15$ and diameter
$\le 10$ have been found by computer search among Cayley graphs
of semidirect products of cyclic groups. We show that {\it all}
of them can in fact be described as lifts of smaller Cayley graphs
of cyclic groups, with voltages in (other) cyclic groups.
This opens up a new possible direction in the
search for large vertex-transitive graphs of
given degree and diameter.



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