Clar Theory for Hexagonal Benzenoids with Corner Defects

We present here a study of Clar covering polynomials (aka Zhang-Zhang or ZZ polynomials) for a family of structural derivatives of hexagonal benzenoids O (n1; n2; n3) with some of its corners removed. This family consists of 64 dis-tinct structures. The ZZ polynomials of structures in this family are interrelated by a network of 192 algebraic recurrence relations. Symmetry considerations allow us to reduce the studied network to 96 recurrence relations involving 36 symmetry-distinct structures. Equations dening 25 of these structures are purely algebraic and can be completely solved. The ZZ polynomials of the remaining 11 structures, interrelated by 15 recurrence relations, are characterized in terms of generating function for one of these structures, e.g., O (n1; n2; n3). The presented result is not fully satisfactory: one more recurrence relation is missing to nd the explicit form of the generating function for the ZZ polynomials of O (n1; n2; n3). We believe that the presented results constitute an important step toward nding a closed-form ZZ polynomial formulas for hexagonal akes and their derivatives and completing the theory of Clar covers for hexagonal akes.