Courcelle, B., The monadic second-order logic of graphs V: on closing the gap between definability and recognizability, Theoretical Computer Science 80 (1991) 153-202. Context-free graph-grammars are considered such that, in every generated graph (3, a derivation tree of G can be constructed by means of monadic second-order formulas that specify its nodes, its labels, the successors of a node e...

Effect of CO2-related acidification on aspects of the larval development of the European lobster, Homarus gammarus (L.) K. E. Arnold, H. S. Findlay, J. I. Spicer, C. L. Daniels, and D. Boothroyd National Lobster Hatchery, South Quay, Padstow, Cornwall, PL28 8BL, UK Plymouth Marine Laboratory, Prospect Place, West Hoe, Plymouth, Devon, PL1 3DH, UK Marine Biology and Ecology Research Centre, Scho...

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We prove that we can specify by formulas of monadic second-order logic the unique planar embedding of a 3-connected planar graph. If the planar graph is not 3-connected but given with a linear order of its set of edges, we can also define a planar embedding by monadic second-order formulas. We cannot do so in general without the ordering, even for 2-connected planar graphs. The planar embedding...

This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs hav...

The rigidity of squares of graphs in three-space has important applications to the study of flexibility in molecules. The Molecular Conjecture, posed in 1984 by T-S. Tay and W. Whiteley, states that the square G of a graph G of minimum degree at least two is rigid if and only if G has six spanning trees which cover each edge of G at most five times. We give a lower bound on the degrees of freed...

Ring structures in molecules belong to the most important substructures for many applications in Computational Chemistry. One typical task is to find an implicit description of the ring structure of a molecule. We present efficient algorithms for cyclic graph invariants that may serve as molecular descriptors to accelerate database searches. Another task is to construct a well-defined set of ri...

In this paper, we present a rewriting framework for modeling molecular complexes, biochemical reaction rules and generation of biochemical networks based on the representation of molecular complexes as a particular type of multigraphs with ports called molecular graphs. The advantage of this approach is to obtain for free a rewriting calculus which allows defining at the same level transformati...

A molecular similarity measure has been developed using molecular topological graphs and atomic partial charges. Two kinds of topological graphs were used. One is the ordinary adjacency matrix and the other is a matrix which represents the minimum path length between two atoms of the molecule. The ordinary adjacency matrix is suitable to compare the local structures of molecules such as functio...