Graph theory applications

III. FUZZY GRAPH THEORY APPLICATIONS IN COMPUTER-ASSISTED BIOPOLYMER NMR ASSIGNMENT... 

Isomers are stable chemical compounds with an identical molecular formula but different structure, conformation, or configuration which display different physicochemical properties. The isomer enumeration represents an old graph theory application in chemistry the presentation of the most important isomer enumeration algorithms can be found in a number of reviews. > ... 

Chemical Applications cf Graph Theory, A.T. Balaban (Ed.), Academic Press, London, 1976. 

D. M. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs, Theory and Applications, 3rd edition, Johann Ambrosius Barth Verlag, Heidelberg, 1995. 

In 1967 Harary presented a proof of Polya s Theorem in Chapter 4 of his book [HarF67], and in the following chapter gave some applications. Four years later in Chapter 15 of "Graph Theory" [HarF71] he again gave an exposition of Polya s Theorem and some developments of it. 

Chemical applications of graph theory (A. T. Balaban, ed). Academic Press 1976. 

CatK75 Cattermole, K. W. Graph theory and the telecommunications network. Bull. Inst. Math, and Applications 11 (1975) 94-106. 

Graph Theory and Applications (Y. Alavi, D. R. Lick, A. T. White, eds.) Lecture Notes in Math. 303 Springer 1972. ReaR76 Read, R. C. The enumeration of acyclic chemical compounds. Chap. 4. Chemical Applications of Graph Theory (A. T. Balaban, ed.) Academic Press, 1976. 

Gielen, M. Application of graph theory to the problem of pseudorotation in metall-organic compounds. In Applications of graph theory to chemistry (ed. A. T. Balaban). New York Academic Press (to appear 1972). 

Bertz, S.H. St Sommer, T.f. (1993) Applications of Graph Theory to Synthesis Planning Complexity, Reflexivity, and Vulnerability. In Organic Synthesis Theory and Applications, Vol. 2 (ed. T. Hudhcky), pp. 67-92. lAI Press, Greenwich, CT. 

One may question whether the application of graph theory is really necessary as no doubt a separation such as that described above can be investigated easily without it. However, when more ions are to be separated, the number of nodes grows very rapidly. 

A.T. Balaban, ed.. Chemical Applications of Graph Theory, Academic Press, London, 1976. V. Kvasnicka and J. Pospichal, An improved version of the constructive enumeration of molecular graphs with described sequence of valence states. Chemom. Intell. Lab. Systems, 18 (1993) 171-181. 

Mezey, P.G., Reaction Topology Manifold Theory of Potential Surfaces and Quantum Chemical Synthesis Design, in Chemical Applications of Topology and Graph Theory, Elsevier Sci. 

King, B. (1993) Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry (CRC Press Boca Raton, Ann Arbor). 

Trindle, C, Givan, R. In Chemical Applications of Graph Theory and Topology King, R. B, Ed. Elsevier New York, 1983. Trindle, C. Croatlca Chem. Acta 1984, 57, 1231,... 

To overcome this weakness, we are developing a quantitative structure-activity strategy that is conceptually applicable to all chemicals. To be applicable, at least three criteria are necessary. First, we must be able to calculate the descriptors or Independent variables directly from the chemical structure and, presumably, at a reasonable cost. Second, the ability to calculate the variables should be possible for any chemical. Finally, and most importantly, the variables must be related to a parameter of Interest so that the variables can be used to predict or classify the activity or behavior of the chemical (j ) One important area of research is the development of new variables or descriptors that quantitatively describe the structure of a chemical. The development of these indices has progressed into the mathematical areas of graph theory and topology and a large number of potentially valuable molecular descriptors have been described (7-9). Our objective is not concerned with the development of new descriptors, but alternatively to explore the potential applications of a group of descriptors known as molecular connectivity indices (10). 

A branch of mathematics concerned with the study and applications of graphs and their uses in kinetic behavior of linked processes. Graph theory, especially when applied to the dynamic nature of networks, has provided... 

Johnson, M. (1985) Relating metrics, lines, and variables defined on graphs to problems in medicinal chemistry. In Graph theory and its applications to algorithms and computer science, Alavi, Y., et al. (eds.), John Wiley Sons, New York, pp. 457-470. 

King RB (ed) (1983) Chemical applications of topology and graph theory. Elsevier, Amsterdam, pp 99-123... 

Application of Chemical Graph Theory for the Estimation of the Dielectric Constant of Polyimides... 

The chapter is divided into the following sections. First, a brief introduction to group contribution methods is given with a major emphasis on the concept and limitations of this technique. An introduction to the use of chemical graph theory and how it applies to polymers and in particular to the dielectric constant is given next. Application of the method to a number of polyimides is then demonstrated and predictions are compared to experimental results. 

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