Some Relations Between Kekule Structure and Morgan-Voyce Polynomials

Document Type : Research Paper

Authors

1 Ataturk University

2 bayburt university

Abstract

In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) Morgan-Voyce polynomial equal to the number of k-matchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zig-zag nonbranched catacondensed benzenid chains and Morgan-Voyce polynomials and between regularly zig-zag nonbranched catacondensed benzenid chains and their corresponding caterpillar trees.

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References

  1. R. Tošić, I. Stojmenović, Chemical graphs, Kekulé structures and Fibonacci numbers, Zb. Rad. Prirod.–Mat. Fak. Ser. Mat. 25 (2) (1995) 179–195.
  2. A. T. Balaban, I. Tomescu, Algebratic expressions for the number of Kekulé structure of isoarithmic cata–condensed benzenoid polycyclic hydrocarbons, MATCH Commun. Math. Comput. Chem. 14 (1983) 155–182.
  3. H. Hosoya, Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 44 (1971) 2332–2339.
  4. H. Hosoya, Topological index and Fibonacci numbers with relation to chemistry, Fibonacci Quart.11 (1973) 255–269.
  5. H. Hosoya, Graphical and combinatorial aspects of some orthogonal polynomials, Natur. Sci. Rep. Ochanomizu Univ. 32 (2) (1981) 127–138.
  6. I. Gutman, Topological properties of benzenoid systems. An identity for the sextet polynomial, Theor. Chim. Acta 45 (1977) 309–315.
  7. H. Hosoya, I. Gutman, Kekulé structures of hexagonal chains–some unusual connections, J. Math. Chem. 44 (2008) 559–568.
  8. T. Koshy, Fibonacci and Lucas numbers with applications, Pure and Applied Mathematics (New York), Wiley–Interscience, New York, 2001.
  9. W. J. He, W. C. He, S. L. Xie, Algebratic expressions for Kekulé structure counts of nonbranched cata–condensed benzenoid, Discrete Appl. Math. 35 (1992) 91–106.
  10. R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics. A Foundation for Computer Science, Addison–Wesley, Reading, 1989.
Iranian Journal of Mathematical Chemistry
Volume 8, Issue 2
Special Issue of IJMC on Chemometrics
June 2017
Pages 221-229

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