| Affiliation: | (1) Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, P. R. China;(2) School of Mathematics and Statistics, Lanzhou University, Gansu, Lanzhou, 730000, P. R. China |
| Abstract: | This paper considers the k -resonance of a toroidal polyhex (or toroidal graphitoid) with a string (p, q, t) of three integers (p ≥ 2, q ≥ 2, 0 ≤ t ≤ p − 1). A toroidal polyhex G is said to be k-resonant if, for 1≤ i ≤ k, any i disjoint hexagons are mutually resonant, that is, G has a Kekulé structure (perfect matching) M such that these hexagons are M-alternating (in and off M). Characterizations for 1, 2 and 3-resonant toroidal polyhexes are given respectively in this paper. *This work is supported by FRG, Hong Kong Baptist University; NSFC and TRAPOYT. |
