Counting Clar structures of (4, 6)-fullerenes

Shi, Lingjuan; Zhang, Heping

doi:10.1016/j.amc.2018.10.027

Cited by 4 publications

(1 citation statement)

References 30 publications

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“…More generally, the term fullerene is also used for such graphs where other lengths of faces are present, cf. [21,28]. For instance, the graph (BN ) 16 from Fig.…”

Section: Applicationsmentioning

confidence: 99%

Edge metric dimensions via hierarchical product and integer linear programming

Klavžar¹,

Tavakoli²

2020

Preprint

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If S = {v 1 , . . . , v k } is an ordered subset of vertices of a connected graph G and e is an edge of G, then the vector r G (e|S) = (d G (v 1 , e), . . . , d G (v k , e)) is the edge metric S-representation of e. If the vertices of G have pairwise different edge metric Srepresentations, then S is an edge metric generator for G. The cardinality of a smallest edge metric generator is the edge metric dimension edim(G) of G. A general sharp upper bound on the edge metric dimension of hierarchical products G(U ) ⊓ H is proved. Exact formula is derived for the case when |U | = 1. An integer linear programming model for computing the edge metric dimension is proposed. Several examples are provided which demonstrate how these two methods can be applied to obtain the edge metric dimensions of some applicable graphs.

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“…More generally, the term fullerene is also used for such graphs where other lengths of faces are present, cf. [21,28]. For instance, the graph (BN ) 16 from Fig.…”

Section: Applicationsmentioning

confidence: 99%

Edge metric dimensions via hierarchical product and integer linear programming

Klavžar¹,

Tavakoli²

2020

Preprint

View full text Add to dashboard Cite

show abstract

Edge metric dimensions via hierarchical product and integer linear programming

Klavžar

Tavakoli

2020

Optim Lett

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Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-Fullerenes C52–C70

Witek,

Podeszwa

2024

Molecules

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We report an extensive tabulation of several important topological invariants for all the isomers of carbon (5,6)-fullerenes Cn with n = 52–70. The topological invariants (including Kekulé count, Clar count, and Clar number) are computed and reported in the form of the corresponding Zhang–Zhang (ZZ) polynomials. The ZZ polynomials appear to be distinct for each isomer cage, providing a unique label that allows for differentiation between various isomers. Several chemical applications of the computed invariants are reported. The results suggest rather weak correlation between the Kekulé count, Clar count, Clar number invariants, and isomer stability, calling into doubt the predictive power of these topological invariants in discriminating the most stable isomer of a given fullerene. The only exception is the Clar count/Kekulé count ratio, which seems to be the most important diagnostic discovered from our analysis. Stronger correlations are detected between Pauling bond orders computed from Kekulé structures (or Clar covers) and the corresponding equilibrium bond lengths determined from the optimized DFTB geometries of all 30,579 isomers of C20–C70.

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Counting Clar structures of (4, 6)-fullerenes

Cited by 4 publications

References 30 publications

Edge metric dimensions via hierarchical product and integer linear programming

Edge metric dimensions via hierarchical product and integer linear programming

Edge metric dimensions via hierarchical product and integer linear programming

Kekulé Counts, Clar Numbers, and ZZ Polynomials for All Isomers of (5,6)-Fullerenes C52–C70

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