Decomposition of graphical sequences and unigraphs

Abstract

A binary operation o is introduced on the set of graphs and is transferred to graphical sequences. The decomposition theorem stating that any graph and any graphical sequence can be uniquely decomposed into indecomposable components with respect to the operation o is proved. An exhaustive description of the structure of unigraphs based on this theorem is given. © 2000 Elsevier Science B.V. All rights reserved.