A fully benzenoid system has a unique maximum cardinality resonant set |
| |
Authors: | Ivan Gutman Khaled Salem |
| |
Institution: | 1.Faculty of Science,University of Kragujevac,Kragujevac,Serbia;2.Department of Basic Sciences,The British University in Egypt,El Shorouk,Egypt |
| |
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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|