k-resonant benzenoid systems and k-cycle resonant graphs.
A benzenoid system (or hexagonal system) H is said to be k-resonant if, for 1 < or = t < or = k, any t disjoint hexagons of H are mutually resonant; that is, there is a Kekule structure (or perfect matching) K of H such that each of the k hexagons is an K-alternating hexagon. A connected graph G is said to be k-cycle resonant if, for 1 < or = t < or = k, any t disjoint cycles in G are mutually resonant. The concept of k-resonant benzenoid systems is closely related to Clar's aromatic sextet theory, and the concept of k-cycle resonant graphs is a natural generalization of k-resonant benzenoid systems. Some necessary and sufficient conditions for a benzenoid system (respectively a graph) to be k-resonant (respectively k-cycle resonant) have been established. In this paper, we will give a survey on investigations of k-resonant benzenoid systems and k-cycle resonant graphs.
Guo
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X
Institute of Mathematics and Physics, Xinjiang University, Wulumuqi Xinjiang 830046, People's Republic of China. xfguo@xju.edu.cn
Zhang
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F