Novel Indices for the Topological Complexity of Molecules

References

• Balaban , A. T. , Motoc , I. , Bonchev , D. and Mekenyan , O. 1983 . “ Topological indices for QSAR ” . In Topics Curr. Chen. , Vol. 114 , 21 – 56 . Berlin : Springer .
   Google Scholar
• Rouvray , D. H. 1987 . The modeling of chemical phenomena using topological indices. . J. Comput. Chem. , 8 : 470 – 480 .
   Web of Science ®Google Scholar
• Rouvray , D. H. 1989 . The limits of applicability of topological indices. . Theochem. , 185 : 187
   Google Scholar
• Stankevich , M. I. , Stankevich , I. V. and Zefirov , N. S. 1988 . Topological indices in organic chemistry. . Usp. Khim. , 57 : 337 – 366 .
   Google Scholar
• 1975 . Communications in Mathematical Chemistry (MATCH) , Mülheim(Ruhr) . founded in, by O. E. Polansky.
   Google Scholar
• Rouvray , D. H. , ed. Journal of Mathematical Chemistry , International Society for Mathematical Chemistry . founded in 1987 by the, first editor
   Google Scholar
• Bonchev , D. and Rouvray , D. H. , eds. 1990–1997 . Mathematical Chemistry , Vol. 1–5 , Chichester, , U.K. : Gordon and Breach .
   Google Scholar
• Trinajstić , N. 1992 . Chemical Graph Theory , 2nd revised ed. Boca Raton, FL : CRC Press .
   Google Scholar
• Randić , M. 1975 . On characterization of molecular branching. . J. Am. Chem. Soc. , 97 : 6609 – 6615 .
   Web of Science ®Google Scholar
• Kier , L. B. , Hall , L. H. , Murray , W. J. and Randić , M. 1975 . Molecular connectivity I, Relationship to nonspecific local anesthesia. . J. Pharm. Sci. , 64 : 1971 – 1974 .
   PubMed Web of Science ®Google Scholar
• Kier , L. B. and Hall , L. H. 1976 . Molecular Connectivity in Chemistry and Drug Research , New York : Academic Press .
   Google Scholar
• Kier , L. B. and Hall , L. H. 1986 . Molecular Connectivity in Structure-Activity Analysis , Chichester : Research Studies Press .
   Google Scholar
• Wiener , H. 1947 . Structural determination of paraffin boiling points. . J. Am. Chem. Soc. , 69 : 17 – 20 .
   PubMed Web of Science ®Google Scholar
• Wiener , H. 1948 . Relation of the physical properties of the isomeric alkanes to molecular structure. . J. Phys. Chem. , 52 : 1082 – 1089 .
   Web of Science ®Google Scholar
• Kier , L. B. and Testa , B. 1995 . Complexity and emergence in drug research. . Adv. Durg Res. , 26 : 1 – 43 .
   Google Scholar
• Bonchev , D. and Seitz , W. A. 1996 . “ The concept of complexity in chemistry. ” . In Concepts in Chemistry: Contemporary Challenge , Edited by: Rouvray , D. H. 353 – 381 . Taunton, , U. K. : Research Studies Press .
   Google Scholar
• Dancoff , S. M. and Kastler , H. 1953 . “ The information content and error rate of living things. ” . In Essays on the Use of Information Theory in Biology , Edited by: Kastler , H. Urbana : University of Illinois Press .
   Google Scholar
• Linshitz , H. 1953 . “ The information content of a bacterial cell. ” . In Essays on the Use of Information Theory in Biology , Edited by: Kastler , H. Urbana : University of Illinois press .
   Google Scholar
• Rashevsky , N. 1955 . Life, information theory, and topology. . Bull. Math. Biophys. , 17 : 229 – 235 .
   Google Scholar
• Trucco , E. 1956 . A note on the information content of graphs. . Bull Math. Biophys. , 18 : 129 – 135 .
   Google Scholar
• Trucco , E. 1956 . On the information content of graphs. Compound symbols; Different states for each point. . Bull Math. Biophys. , 18 : 237 – 253 .
   Google Scholar
• Rashevsky , N. 1960 . Life, information theory, probability, and physics. . Bull. Math. Biophys. , 22 : 351 – 364 .
   Google Scholar
• Mowshovitz , A. 1968 . Entropy and the complexity of graphs. 1. An index of the relative complexity of a graph. . Bull. Math. Biophys. , 30 : 175 – 204 .
   PubMedGoogle Scholar
• Shannon , C. and Weaver , W. 1949 . Mathematical Theory of Communications. , Urbana, MI : University of Illinois Press .
   Google Scholar
• Bonchev , D. and Trinajstić , N. 1977 . Information theory, distance matrix, and molecular branching. . J. Chem. Phys. , 67 : 4517 – 4533 .
   Web of Science ®Google Scholar
• Bonchev , D. 1983 . Information Theoretic Indices for Characterization of Chemical Structures. , Chichester, , U.K. : Research Studies press .
   Google Scholar
• Bertz , S. H. 1981 . The First General Index of Molecular Complexity. . J. Am. Chem. Soc. , 103 : 3599 – 3601 .
   Web of Science ®Google Scholar
• Bertz , S. H. 1983 . On the complexity of graphs and molecules. . Bull Math. Biol. , 45 : 849 – 855 .
   Google Scholar
• Randić , M. , Kraus , A. G. and Džonova;-Jerman-Blažić , B. 1983 . “ Ordering of graphs as an approach to structure-activity studies. ” . In Chemical Applications of Topology and Graph Theory , Edited by: King , R. B. 192 – 205 . Amsterdam : Elsevier .
   Google Scholar
• Bonchev , D. and Kier , L. B. 1992 . Topological atomic indices and the electron charges in alkanes. . J. Math. Chem. , 9 : 75 – 85 .
   Web of Science ®Google Scholar
• Mekenyan , O. and Bonchev , D. 1985 . Molecular structure descriptors and biological activity. In FECS Third International Conference on Chemistry and Biotechnology of Biologically Active Natural Products . Bulg. Acad. Sci., Sofia , 3 : 365 – 369 .
   Google Scholar
• Randić , M. 1988 . On characterization of three-dimensional structures. . Int. J. Quant. Chem. Quant. Biol. Symp. , 15 : 201 – 208 .
   Google Scholar
• Randić , M. , Jerman-Blažić , B. and Trinajstić , N. 1990 . Development of 3-dimensional molecular descriptors. . Comput. Chem. , 14 : 237 – 246 .
   Google Scholar
• Bonchev , D. , Mekenyan , O. and Trinajstić , N. 1981 . Isomer discrimination by topological information approach. . J. Comput. Chem. , 2 : 127 – 148 .
   Google Scholar
• Raychaudhury , C. , Ray , S. K. , Ghosh , J. J. , Roy , A. B. and Basak , S. C. 1984 . Discrimination of isomeric structures using information theoretic topological indices. . J. Comput. Chem. , 5 : 581 – 588 .
   Web of Science ®Google Scholar
• Bonchev , D. and Polansky , O. E. 1987 . “ On the topological complexity of chemical systems. ” . In Graph Theory and Topology in Chemistry , Edited by: King , R. B. and Rouvray , D. H. 126 – 158 . Amsterdam : Elsevier .
   Google Scholar
• Minoli , D. 1976 . Atti. Acad. Waz. Lincei Rend. , A59 : 154
   Google Scholar
• Bonchev , D. , Mekenyan , O. and Trinajstic , N. 1980 . Topological characterization of cyclic structures . Int. J. Quantum Chem. , 17 : 845 – 893 .
   Web of Science ®Google Scholar
• Mekenyan , O. , Bonchev , D. and Trinajstić . 1983 . Structural complexity and molecular properties of cyclic molecules with acyclic branches. . Croat. Chem. Acta , 56 : 237 – 261 .
   Google Scholar
• Mekenyan , O. , Bonchev , D. and Trinajstic , N. 1980 . Chemical graph theory modeling the thermodynamic properties of molecules. . Intern. J. Quantum Chem. Symp. , 18 : 369 – 380 .
   Google Scholar
• Bonchev , D. , Kamenska , V. and Mekenyan , O. 1990 . Comparability graphs and molecular properties: IV. Generalizations and applications. . J. Math. Chem. , 5 : 43 – 72 .
   Google Scholar
• Bonchev , D. , Mekenyan , O. and Fritsche , H. 1980 . An approach to the topological modeling of crystal growth. . J. Cryst. Growth , 49 : 90 – 96 .
   Google Scholar
• Bonchev , D. , Mekenyan , O. and Kamenska , V. 1992 . A topological approach to the modeling of polymer properties (The TEMPO method). . J. Math. Chem. , 11 : 107 – 132 .
   Google Scholar
• Bonchev , D. , Balaban , A. T. and Mekenyan , O. 1980 . Generalization of the graph center concept, and derived topological indexes. . J. Chem. Inf. Comput. Sci. , 20 : 106 – 113 .
   Google Scholar
• Bonchev , D. 1989 . The concept for the centre of a chemical structure and its applications. . Theochem. , 185 : 155 – 168 .
   Google Scholar
• Bertz , S. H. 1989 . Branching in graphs and molecule . Discr. Appl. Math. , 19 : 65 – 83 .
   Google Scholar
• Bertz , S. H. 1989 . “ A mathematical model of molecular complexity. ” . In Chemical Applications of Topology and Graph Theory , Edited by: King , R. B. 206 – 221 . Amsterdam : Elsevier .
   Google Scholar
• Bonchev , D. 1990 . “ The problems of computing molecular complexity. ” . In Computational Chemical Graph Theory , Edited by: Rouvray , D. H. 34 – 67 . New York : Nova .
   Google Scholar
• Gordon , M. and Kennedy , J. W. 1973 . The graph-like state of matter. Part 2. TCGI schemes for the thermodynamics of alkanes and the theory of inductive inference. . J. C. S. Faraday Trans. II , 69 : 484 – 504 .
   Google Scholar
• Bertz , S. and Herndon , W. C. 1986 . Similarity of Graphs and Molecules. . Artificial Intelligence Applications in Chemistry , : 169 – 175 .
   Google Scholar
• Bonchev and Kolmogorov's , D. information, Shannon's entropy, and topological complexity of molecules. . Bulg. Chem. Commun , (in press)
   Google Scholar
• Bonchev , D. 1995 . Topological order in molecules. 1. Molecular branching revisited . Theochem. , 336 : 137 – 156 .
   Google Scholar
• Mekenyan , O. , Karabunarliev , S. and Bonchev , D. 1990 . The OASIS concept for predicting biological activity of chemical compounds. . J. Math. Chem. , 4 : 207 – 215 .
   Web of Science ®Google Scholar
• Bonchev , D. , Mountain , C. F. , Seitz , W. A. and Balaban , A. T. 1993 . Modeling the anticancer action of some retinoid compounds by making use of the OASIS method. . J. Med. Chem. , 36 : 1562 – 1569 .
   PubMed Web of Science ®Google Scholar
• Balaban , A. T. 1983 . Topological indices based on topological distances in molecular graphs. . Pure Appl. Chem. , 55 : 199 – 206 .
   Web of Science ®Google Scholar
• Gutman , I. , Ruščić , B. , Trinajstić , N. and Wilcox , C. F. 1975 . Graph theory and molecular orbitals. . J. Chem. Phys. , 62 : 3399 – 1405 .
   Web of Science ®Google Scholar