TY - JOUR
T1 - Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures
T2 - Chevrons and generalized chevrons
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).
UR - http://www.scopus.com/inward/record.url?scp=84898712025&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84898712025
SN - 0166-218X
VL - 198
SP - 101
EP - 108
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 1
ER -