TY - JOUR

T1 - Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures

T2 - Prolate rectangles and their generalizations

AU - Chou, Chien Pin

AU - Witek, Henryk A.

PY - 2016/1/10

Y1 - 2016/1/10

N2 - We show that the Zhang-Zhang (ZZ) polynomial of a benzenoid obtained by fusing a parallelogram M(m,n) with an arbitrary benzenoid structure ABC can be simply computed as a product of the ZZ polynomials of both fragments. It seems possible to extend this important result also to cases where both fused structures are arbitrary Kekuléan benzenoids. Formal proofs of explicit forms of the ZZ polynomials for prolate rectangles Pr(m,n) and generalized prolate rectangles Pr([m1,m2,⋯, mn],n) follow as a straightforward application of the general theory, giving ZZ(Pr(m,n),x)=(1+(1+x)·m)n and ZZ(Pr([m1,m2,⋯, mn],n),x)=π;k=1 n(1+(1+x )· mk).

AB - We show that the Zhang-Zhang (ZZ) polynomial of a benzenoid obtained by fusing a parallelogram M(m,n) with an arbitrary benzenoid structure ABC can be simply computed as a product of the ZZ polynomials of both fragments. It seems possible to extend this important result also to cases where both fused structures are arbitrary Kekuléan benzenoids. Formal proofs of explicit forms of the ZZ polynomials for prolate rectangles Pr(m,n) and generalized prolate rectangles Pr([m1,m2,⋯, mn],n) follow as a straightforward application of the general theory, giving ZZ(Pr(m,n),x)=(1+(1+x)·m)n and ZZ(Pr([m1,m2,⋯, mn],n),x)=π;k=1 n(1+(1+x )· mk).

KW - Clar cover

KW - Clar structure

KW - Perfect matching

KW - Zhang-Zhang polynomial

UR - http://www.scopus.com/inward/record.url?scp=84936806586&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2015.06.020

DO - 10.1016/j.dam.2015.06.020

M3 - Article

AN - SCOPUS:84898712025

SN - 0166-218X

VL - 198

SP - 101

EP - 108

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -