Results

**1 - 3**of**3**### A Constructive Enumeration of Fusenes and Benzenoids

"... In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using ..."

Abstract
- Add to MetaCart

In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using the canonical construction path method and the homomorphism principle.

### Pohang 790–784, The Republic of Korea

"... A very brief survey of the main results concerning the cell–growth problem and its variations is given. The name stems from an analogy with an animal which, starting from a single cell of some specified basic polygonal shape, grows step by step in the plane by adding at each step a cell of the same ..."

Abstract
- Add to MetaCart

(Show Context)
A very brief survey of the main results concerning the cell–growth problem and its variations is given. The name stems from an analogy with an animal which, starting from a single cell of some specified basic polygonal shape, grows step by step in the plane by adding at each step a cell of the same shape to its periphery. The fundamental combinatorial problem concerning these animals is ”How many animals with n cells are there? ” This problem was included in the list of unsolved problems in the enumeration of graphs by Frank Harary in 1960. Despite serious efforts over the last 40 years, this problem is completely open. However, a few asymptotic results are known. For example, let p(n) denote the number of polyominoes (square animals) having n cells. It was proved that (p(n)) 1/n tends to a limit Θ, which satisfies the following inequality: 3.87 < Θ < 4.65. The situation could hardly be worse, since the first digit of Θ is not even known... The difficulty of the classical cell–growth problem has led to the study of various restricted classes of polyominoes. Some variations of this problem are considered. Unsolved problems are stated. Chemical applications of this problem are mentioned too. 1. Classical cell–growth problem