K-resonance in toroidal polyhexes

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.