On linearizing graphs

Abstract

The notion of addressing scheme Rosenberg [5] established in his theory of data graphs and addressing schemes is used as a linearizing concept for labelled graphs. The equivalence of this concept to the graph-specification model Culik II and Maurer [2] developed to describe so called selector-graphs in a linear way is shown. Further, two constructions which modify weakly non-linearizable graphs such that their modification are linearizable are given. Some considerations on the classification of the linearizations of labelled graphs in the sense of formal language theory are made and it is proved that the class of R-regular graphs possesses regular linearizations. Finally some results concerning operations on graphs which preserve linearizability and how linearizations of graphs can be represented by two parts such that one of them is finite are given.