Abstract
We study a random planar honeycomb lattice model, namely the random double hexagonal chains. This is a lattice system with nonperiodic boundary condition. The Wiener number is an important molecular descriptor based on the distances, which was introduced by the chemist Harold Wiener in 1947. By applying probabilistic method and combinatorial techniques we obtained an explicit analytical expression for the expected value of Wiener number of a random double hexagonal chain, and the limiting behaviors on the annealed entropy of Wiener number when the random double hexagonal chain becomes infinite in length are analyzed.
Highlights
Topological indices based on the distances between the vertices of a graph are widely used in theoretical chemistry to establish relations between the structure and the properties of molecules and provide correlations with physical, chemical, and thermodynamic parameters of chemical compounds [1]
By applying probabilistic method and combinatorial techniques we obtained an explicit analytical expression for the expected value of Wiener number of a random double hexagonal chain, and the limiting behaviors on the annealed entropy of Wiener number when the random double hexagonal chain becomes infinite in length are analyzed
We study the annealed entropy of Wiener number on random double hexagonal chains
Summary
Topological indices (molecular structure descriptors) based on the distances between the vertices of a graph are widely used in theoretical chemistry to establish relations between the structure and the properties of molecules and provide correlations with physical, chemical, and thermodynamic parameters of chemical compounds [1]. In [4], Gutman et al obtained an explicit analytical expression for the expected value of the Wiener number of a random benzenoid chain with n hexagons(a graph of unbranched catacondensed benzenoid-like structure). We study the annealed entropy of Wiener number on random double hexagonal chains. The random double hexagonal chain RD2×n can be obtained from a naphthalene by stepwise triple-edge fusion of a new naphthalene. By applying probabilistic method and combinatorial techniques an explicit analytical expression for the expected value ( ) ( ) n = W ( RD2×n ) of the Wiener number of a random double hexagonal chain with n naphthalenes is obtained. The limiting behaviors on the annealed entropy of Wiener number when the random double hexagonal chain becomes infinite in length are analyzed
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