Abstract
By applying information theory to the set of topological distances from one vertex to all other graph vertices, one obtains four new types of vertex invariants (u i,v i,x i,Y i) which are real numbers (as opposed to integers). They may be combined in many ways to afford new topological indices. One such type leads to indicesU, V, X andY which show no degeneracy for alkanes with up to 15 vertices.
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A.T. Balaban, I. Motoc, D. Bonchev and O. Mekenyan, Top. Curr. Chem. 21 (1983) 114.
A.T. Balaban, Pure Appl. Chem. 55 (1983) 199.
A.T. Balaban, Revista de Chimie 39 (1988) 1026.
A.T. Balaban, A. Chiriac, I. Motoc and Z. Simon,Steric Fit in QSAR Lecture Notes in Chemistry Vol. 15 (Springer, Berlin 1980).
M.I. Stankevitch, I.V. Stankevitch and N.S. Zefirov, Usp. Khim. 57 (1988) 337.
E. Hladka and L. Matyska, Chem. Listy 82 (1988) 1009.
A. Sabljić and N. Trinajstić Acta Pharm. Jugosl. 31 (1982) 189.
D.H. Rouvray, Sci. Amer. 255 (Sept., 1986).
L.B. Kier and L.H. Hall,Molecular Connectivity in Chemistry and Drug Research (Academic Press, New York, 1983);Molecular Connectivity in Structure-Activity Analysis (Wiley, New York, 1986).
S.H. Bertz, Discr. Appl. Math. 19 (1988) 65, reprinted in:Applications of Graphs in Chemistry and Physics, ed. J.W. Kennedy and L.V. Quintas (North-Holland, Amsterdam, 1988).
A.T. Balaban, J. Mol. Struct. (THEOCHEM) 165 (1988) 243.
W. Herndon and J.E. Leonard, Inorg. Chem. 22 (1983) 554.
M. Randić, J. Chem. Inf. Comput. Sci. 24 (1984) 164.
A.T. Balaban, Chem. Phys. Lett. 89 (1982) 339.
O. Mekenyan, D. Bonchev and A.T. Balaban, J. Comput. Chem. 5 (1984) 629.
P.A. Filip], T.-S. Balaban and A.T. Balaban, J. Math. Chem. 1 (1987) 61.
V.E. Gollender, V.V. Drboglav and A.B. Rosenblit, J. Chem. Inf. Comput. Sci. 21 (1981) 196.
O. Mekenyan, D. Bonchev and A.T. Balaba, J. Math. Chem. 2 (1988) 347.
H. Wiener, J. Amer. Chem. Soc. 69 (1947) 2636; J. Chem. Phys. 15(1947)766.
D. Bonchev and N. Trinajstić, J. Chem. Phys. 67 (1977) 4517;Int. J. Quant. Chem. Symp. 12(1978)293; idem 16(1982)463.
D. Bonchev, O. Mekenyan and N. Trinajstić, J. Comput. Chem. 2 (1981) 127.
D. Bonchev,Information Theoretic Indices for Characterization of Chemical Strctures (Research Studies Press, Chichester, 1983).
C. Raychaudhury, S.K. Ray, J.J. Gosh, A.B. Roy and S.C. Basak, J. Comput Chem. 5 (1984) 581; G. Klopman and C. Raychaudhury, ibid. 9(1988)232; J. Chem. Inf. Comput. Sci. 30(1990)12; Bull. Soc. Chim. Belg. 99(1990)225; C. Raychaudhury, S.C. Basak, A.B. Roy and J.J. Ghosh, Indian Drugs 18(1980)97; S.K. Roy, S.C. Basak, C. Raychaudhury, A.B. Roy and J.J. Ghosh, Arzneim.-Forsch. 32(1982)322; 33(1983)352; Indian J. Pharmacol. 13(1982)301; R. Sarkar, A.B. Roy and P.K. Sarkar, Math. Bio. Sci. 39(1978)229; A.B. Roy, C. Raychaudhury, J.J. Ghosh, S.K. Roy and S.C. Basak, in:Quantitative Approaches to Drug Design, ed. J.C. Dearden (Elsevier, Amsterdam, 1983), p. 75.
M. Randić, J. Amer. Chem. Soc. 97 (1975) 6609.
M. Randić, J. Chem. Inf. Comput. Sci. 18 (1978) 101
Note added in proof: 4-Trees with 18 vertices may beU, V, X andY degenerate, as will be shown: O. Ivanciuc, T.-S. Balaban and A.T. Balaban, J. Math. Chem., submitted.
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Balaban, A.T., Balaban, TS. New vertex invariants and topological indices of chemical graphs based on information on distances. J Math Chem 8, 383–397 (1991). https://doi.org/10.1007/BF01166951
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DOI: https://doi.org/10.1007/BF01166951