Abstract
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){dot operator}m)n and ZZ(Pr([m1,m2,. .,mn],n),x)=∏k=1n(1+(1+x){dot operator}mk).
| Original language | English |
|---|---|
| Journal | Discrete Applied Mathematics |
| DOIs | |
| Publication status | Accepted/In press - 2014 Sep 18 |
| Externally published | Yes |
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Keywords
- Clar cover
- Clar structure
- Perfect matching
- Zhang-Zhang polynomial
ASJC Scopus subject areas
- Applied Mathematics
- Discrete Mathematics and Combinatorics
Cite this
Closed-form formulas for the Zhang-Zhang polynomials of benzenoid structures : Prolate rectangles and their generalizations. / Chou, Chien Pin; Kang, Jin Su; Witek, Henryk A.
In: Discrete Applied Mathematics, 18.09.2014.Research output: Contribution to journal › Article
}
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 - Kang, Jin Su
AU - Witek, Henryk A.
PY - 2014/9/18
Y1 - 2014/9/18
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){dot operator}m)n and ZZ(Pr([m1,m2,. .,mn],n),x)=∏k=1n(1+(1+x){dot operator}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){dot operator}m)n and ZZ(Pr([m1,m2,. .,mn],n),x)=∏k=1n(1+(1+x){dot operator}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
UR - http://www.scopus.com/inward/citedby.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:84936806586
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
ER -