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| Content Provider | Springer Nature Link |
|---|---|
| Author | Salem, Khaled Gutman, Ivan |
| Copyright Year | 2009 |
| Abstract | A benzenoid system is a 2-connected plane graph such that its each inner face is a regular hexagon of side length 1. A benzenoid system is Kekuléan if it has a perfect matching. Let P be a set of hexagons of a Kekuléan benzenoid system B. The set P is called a resonant set of B if the hexagons in P are pair-wise disjoint and the subgraph B−P (obtained by deleting from B the vertices of the hexagons in P) is either empty or has a perfect matching. It was shown (Gutman in Wiss. Z. Thechn. Hochsch. Ilmenau 29:57–65, 1983; Zheng and Chen in Graphs Comb. 1:295–298, 1985) that for every maximum cardinality resonant set P of a Kekuléan benzenoid system B, the subgraph B−P is either empty or has a unique perfect matching. A Kekuléan benzenoid system B is said to be fully benzenoid if there exists a maximum cardinality resonant set P of B, such that the subgraph B−P is empty. It is shown that a fully benzenoid system has a unique maximum cardinality resonant set, a well-known statement that, so far, has remained without a rigorous proof. |
| Ending Page | 19 |
| Page Count | 5 |
| Starting Page | 15 |
| File Format | |
| ISSN | 01678019 |
| e-ISSN | 15729036 |
| Journal | Acta Applicandae Mathematica |
| Issue Number | 1 |
| Volume Number | 112 |
| Language | English |
| Publisher | Springer Netherlands |
| Publisher Date | 2009-10-06 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Applications Theoretical, Mathematical and Computational Physics Computer Science Mechanics Benzenoid system Mathematics Resonant set Clar formula Statistical Physics, Dynamical Systems and Complexity Perfect matching |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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