两种四角系统的Wiener数和Hyper-Wiener数(英文)论文
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最后更新时间:2024-03-03
AbstractIn this paper we deduce the formula of Wiener number and Hyper-Wiener number of two types of polyomino systems.
Key wordsWiener number； Hyper-Wiener number； Polyomino systems
CLC numberO 15
The topological index W， conceived by Wiener[1]more than half a century ago， is one of the most thoroughly studied in chemical graph. Let G be a graph， Wiener number W（G） is defined as follows： Let u and v be two vertices of G， the distance between u and v is equal to the length of a shortest path that connects u and v in the graph G， which is denoted by d（u，v）. The Wiener number is equal to the sum of the distances between all pairs of vertices of G，
In this section， we Calculate the Wiener number and Hyper-Wiener number of two types of polyomino systems.
（1）Thefirst type of polyomino system is shown in Figure 1. It is a polyomino chain.
[1] Wiener H. Structural determination of paraffin boiling points. J Am Chem Soc， 1947， 69： 17-20.
[2] Shiu W C， Lam P C B. Wiener numbers of some pericondensed benzenoid molecule systems. Congrseeus Numerantium， 1997， 126： 113-124.
[3] Gutman I， Yeh Y N， Lee S L， Luo Y L. Some recent results in the theory of the Wiener number. Indian Journal of Chemistry， 1993， 32A： 651-661.
[4] Gutman I， Potgieter J H. Wiener index and intermolecular forces. J Serb Chem Soc， 1997， 62（3）： 185-192.
[5] Gutman I， Klzar S. A method for calculating Wiener numbers of benzenoid hydrocarbons. Models in Chemistry， 1996， 133（4）：389-399.
[7] Gutman I， Klzar S. Relations between Wiener numbers of benzenoid hydrocarbons and phenylenes. Models in Chemistry， 1998， 135（1-2）： 45-55.
[8] Randic M. Novel molecular descriptor for structure-property studies. Chem Phys Lett， 1993， 211： 478-483.
[9] Klein D， Lukovits J， Gutman I. On the definition of the Hyper-Wiener index for cyclecontaining structures. J Chem Inf Comput Sci， 1995， 35： 50-52.
[10] Hosoya H. On some counting polynomials in chemistry. Discrete Appl Math， 1988， 19： 239-257.
[11] Cash G， Klzar S， Petkovsek M. Three Methods for Calculation of the Hyper-Wiener index of Molecular Graphs. J Chem Inf Comput Sci， 2002， 42（3）： 571-576.
[12] Pan Y J. Wiener number of polyomino chains. Journal of Xinjiang university， 2006， 23： 90-95.
Key wordsWiener number； Hyper-Wiener number； Polyomino systems
CLC numberO 15
7.6Document codeA
1IntroductionThe topological index W， conceived by Wiener[1]more than half a century ago， is one of the most thoroughly studied in chemical graph. Let G be a graph， Wiener number W（G） is defined as follows： Let u and v be two vertices of G， the distance between u and v is equal to the length of a shortest path that connects u and v in the graph G， which is denoted by d（u，v）. The Wiener number is equal to the sum of the distances between all pairs of vertices of G，
In this section， we Calculate the Wiener number and Hyper-Wiener number of two types of polyomino systems.
（1）Thefirst type of polyomino system is shown in Figure 1. It is a polyomino chain.
[1] Wiener H. Structural determination of paraffin boiling points. J Am Chem Soc， 1947， 69： 17-20.
[2] Shiu W C， Lam P C B. Wiener numbers of some pericondensed benzenoid molecule systems. Congrseeus Numerantium， 1997， 126： 113-124.
[3] Gutman I， Yeh Y N， Lee S L， Luo Y L. Some recent results in the theory of the Wiener number. Indian Journal of Chemistry， 1993， 32A： 651-661.
[4] Gutman I， Potgieter J H. Wiener index and intermolecular forces. J Serb Chem Soc， 1997， 62（3）： 185-192.
[5] Gutman I， Klzar S. A method for calculating Wiener numbers of benzenoid hydrocarbons. Models in Chemistry， 1996， 133（4）：389-399.
[7] Gutman I， Klzar S. Relations between Wiener numbers of benzenoid hydrocarbons and phenylenes. Models in Chemistry， 1998， 135（1-2）： 45-55.
[8] Randic M. Novel molecular descriptor for structure-property studies. Chem Phys Lett， 1993， 211： 478-483.
[9] Klein D， Lukovits J， Gutman I. On the definition of the Hyper-Wiener index for cyclecontaining structures. J Chem Inf Comput Sci， 1995， 35： 50-52.
[10] Hosoya H. On some counting polynomials in chemistry. Discrete Appl Math， 1988， 19： 239-257.
[11] Cash G， Klzar S， Petkovsek M. Three Methods for Calculation of the Hyper-Wiener index of Molecular Graphs. J Chem Inf Comput Sci， 2002， 42（3）： 571-576.
[12] Pan Y J. Wiener number of polyomino chains. Journal of Xinjiang university， 2006， 23： 90-95.