The slope variety of a graph is an algebraic set whose points correspond to drawings of that graph. A complement-reducible graph (or cograph) is a graph without an induced four-vertex path. We construct a bijection between the zeroes of the slope variety of the complete graph on n vertices over F2, and the complementreducible graphs on n vertices.

The present work aims to exploit the interplay between algebraic properties of rings and graph-theoretic structures some associated graphs. We introduce commutatively closed graphs investigate subsets a ring with help graph theory. In particular, we compute diameter matrix Artinian semisimple algebras.

Graph transformation systems have been introduced for the formal specification of software systems. States are thereby modeled as graphs, and computations as graph derivations according to the rules of the specification. Operations on graph derivations provide means to reason about the distribution and composition of computations. In this paper we discuss the development of an algebra of graph ...

We consider a weighted communication graph in a network of mobile robots, and its associated Laplacian whose entries depend on the pairwise distance between the robots. We propose a heuristic distributed solution for the maximization of the algebraic connectivity of the graph by moving the robots to appropriate positions. Our approach is optimization-based and can be extended to handle various ...

We report on an adapted version of the Bentley-Ottmann algorithm for computing all the intersection points among the edges of the projection of a three-dimensional graph. This graph is given as a set of vertices together with their space Euclidean coordinates, and a set of edges connecting them. More precisely, the three-dimensional graph represents the approximation of a closed and smooth impl...