On transitive decompositions of disconnected graphs

Abstract: We investigate transitive decompositions of disconnected graphs, and show that these behave very differently from a related class of algebraic graph decompositions, known as homogeneous factorisations. We conclude that although the study of homogeneous factorisations admits a natural reduction to those cases where the graph is connected, the study of transitive decompositions does not. [Copyright &y& Elsevier]