Bicoset groups and symmetric graphs

In this paper, we construct a functor from the set of bicoset multivalued groups with one Hermitian generator to the set of symmetric graphs. The functor makes it possible to describe the set of bicoset multivalued groups with one Hermitian generator as a sum of categories. The categories are indexed by pairs (^U,G^U), where ^U is a universal symmetric graph and G^U is a subgroup of Aut(^U). Bibliography: 5 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 292, 2002, pp. 161–174.This revised version was published online in April 2005 with a corrected cover date and article title.