We define the concept of a k-twisted chain in a (directed) graph and the concept of a 2k-twisted graph. We show that for a 2k-twisted graph the set of algebraic 2k-twisted cycles is an integral spanning set for the integral flow module of G. Since a graph is O-twisted if and only if it is strongly connected, our result generalizes the well-known theorem that there is a basis for the flow space ...

In this paper, we propose a new framework of model transformation that combines graph transformation with algebraic specification. While graph transformation is well-suited to describe the transformation of visual models, one can observe that models are often composite structures with visual, graphical and diagrammatic components accompanied by all kinds of data objects like strings, sets, numb...

Grammatica is a prototype implementation of algebraic graph transformation based on relation algebra. It has been implemented using Mathematica on top of the Combinatorica package, and runs therefore on most platforms. It consists of Mathematica routines for representing, manipulating, displaying and transforming graphs, as well as routines implementing some relation algebra-theoretic operation...

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.

We define collagories essentially as “distributive allegories without zero morphisms”, and show that they are sufficient for accommodating the relation-algebraic approach to graph transformation. Collagories closely correspond to the adhesive categories important for the categorical DPO approach to graph transformation. but thanks to their relation-algebraic flavour provide a more accessible an...