Graph-theory derived model

The topological homeomorphism of a deltahedron to a sphere used in the graph-theory-derived models is also the basis of the tensor surface harmonic theory devel-... 

The core and surface orbitals defined above by tensor surface harmonic theory can be related to the following aspects of the graph-theory-derived model for the skeletal bonding in boranes with the deltahedral structures depicted in Figure 4 ... 

Bonding in clusters and condensed cluster compounds that extend in one, two and three dimensions Principles of bonding and reactivity in transition metal cluster compounds Mathematical cluster chemistry Graph-theory derived models for the skeletal chemical bonding in organometallic metal carbonyl clusters... 

Graph-Theory derived Approach Ideas derived from topology and graph-theory are used to model the skeleton chemical bonding in clusters. 29-33... 

We here define our model and present a self-contained introduction to perturbation theory, deriving the Feynman graph representation of the cluster expansion. To deal with solutions of finite concentration we introduce the grand-canonical ensemble and resum the cluster expansion to construct the loop expansion. We Lhen show that without further insight the expansions can be applied only in the (9-region or for concentrated solutions since they diverge term by term in the excluded volume limit. 

Sequences folding into the same structure form neutral networks in sequence space. A mathematical model based on random graph theory was designed [16] in order to allow for the derivation of analytical expressions. Neutral networks are represented by graphs in sequence space that show an interesting percolation phenomenon depending on the... 

Studies using the theory of Quantitative Structure-Activity Relationships (QSAR) are intended to suggest mathematical models capable of estimating the relevant properties of interest, especially when those cannot be experimentally determined for some reason. Such studies rely on the basic assumption that the structure of a compound completely determines its properties, which can therefore be translated into the so-called molecular descriptors. These parameters are calculated through mathematical formulae derived from several theories, such as Chemical Graph Theory, Information... 

The graph method is also useful for theoretical analysis of the models. We will present some theoretical results obtained by using the graph model and applying results from graph theory. In particular, we give a method to determine a minimal set of flow rates in a model and we derive a necessary and sufficient condition for certain systems to be minimal. 

This relationship is the general model of transient diffusion as proposed by the Formal Graph theory. It can be simplified by choosing peculiar conditions. In particular, the multiplication annihilates the space operators for leaving only the time derivation, in assuming as before that the diffusivity is space invariant (homogeneous medium) and that the medium is isotropic ... 

The two matrix representations of the protein segments, the amino acid adjacency matrix and the decagonal isometries matrix, are derived from the sequence information alone. As has been demonstrated, mathematical descriptors, dependent on the sequence information alone, have successfully revealed the underlying characteristics and patterns of given sequences. Their numerical nature also makes them easier to incorporate into a mathematical model. In addition, as has been well illustrated in chemical graph theory, when considering characterization of molecules, one can... 

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