He Wenjie

Generation and enumeration of planar polycyclic aromatic hydrocarbons

Abstract In this paper, we propose a method of the computer generation of all planar polyhexes and display the results of the numbers of polyhexes with up to 9 hexagons.

A novel nomenclature of polycyclic aromatic hydrocarbons without using graph centre

In this paper, we develop a novel adjacency matrix, He-matrix, corresponding to the dualist graph. Without using the graph center concept, we advance a novel nomenclature of polycyclic aromatic hydrocarbons. Further, we derive some distinguishing theorems about PAH molecules and present some results of our automatic derivatization and automatic classification counting of fused PAH molecules.

Enumeration of Benzenoid and Coronoid Hydrocarbons

This is a report on the present status of computer-aided enumeration and classification of benzenoids and coronoids (polyhexes). The existing data from previous works are displayed in comprehensive tables. Numerous data from papers in press are included, as well as original contributions.

One-to-one correspondence between Kekulé and sextet patterns

The concept of super sextet is clarified and the generalized sextet polynomial in two elements is proposed. Two theorems related to Ohkami-Hosoya conjecture [1] are proved and one novel conjecture is proposed.

Topological properties of KHF-graphs and a proof of a one-to-one correspondence between Kekulé and sextet patterns of KHF-graphs

In this paper, the definition of a super sextet is given, the concept of a KHF-graph is proposed, and some of the topological property theorems of KHF-graphs are developed using a similar method as [1]. And so Ohkami-Hosoya conjecture [2] is proved rigorously.

Peak-valley path method on benzenoid and coronoid systems

The present paper is a review of the P-V path method. The concept of the P-V path was proposed by Gordon and Davison in 1952. In the last few years this method has been greatly developed and has become one of the important approaches for investigating Kekule structures of benzenoid hydrocarbons. The superiority of this method is its simplicity and visualization. According to the properties of the P-V path, some algorithmic approaches have been developed for deciding whether a benzenoid or a coronoid hydrocarbon is Kekulean. In 1985, John and Sachs introduced the concept of the P-V matrix and deduced the John-Sachs theorem which states that the absolute value of the determinant of the P-V matrix of a benzenoid or a coronoid hydrocarbon G is equal to the number of Kekule structures of G.

P-V matrix and enumeration of Kekulé structures

In this paper, a simple and intuitive proof of the theorem K= ¦det N(G)¦ [1,2] is given.

Properties of “structure factor” of characteristic polynomial and a proof of Hosoya-Randić conjectures

Some properties of “structure factor” of characteristic polynomial are discussed and Hosoya-Randić conjectures are proved rigorously.

Cut invariant d and bond orders of Kekule´an benzenoids

Abstract In this paper, for benzenoids, the concepts of a Δ cut circuit and a V cut segment are proposed; and for Kekulean benzenoids a cut invariant d corresponding to a Δ cut circuit or a V cut segment is given. The quantity d has a close relation with Pauling bond orders of the cut edges.