Discrimination of Benzenoid Graphs by Topological Polynomials
- 1Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
Abstract
The discrimination of structural isomers remains a central challenge in mathematical chemistry and molecular graph theory. In this work, twenty topological polynomials are evaluated on benzenoid (polyhex) systems containing between four and seven fused hexagons. Computational analysis of all non-isomorphic benzenoid graphs in this range shows that nine descriptors, including the Theta, Matching, Padmakar–Ivan, Vertex–Szeged, Adjacency Characteristic, Laplacian Characteristic, Signless Laplacian Characteristic, Distance Characteristic, and Harary Matrix Characteristic polynomials, exhibit zero degeneracy and uniquely distinguish all 333 benzenoid isomers with seven hexagons. The structural origin of this behavior is investigated through spectral and distance-based graph properties, and a theoretical framework is proposed distinguishing between (i) computationally verified discrimination on finite sets, (ii) exact algebraic properties and finite-domain completeness for catacondensed benzenoids, and (iii) a composite descriptor completeness conjecture. In contrast, Omega, Sadhana, and Zhang–Zhang polynomials display substantial degeneracy, reflecting information loss associated with quasi-orthogonal cut representations. The obtained results identify a class of topological descriptors with exceptional discriminatory capability and potential applicability in QSAR/QSPR modeling, molecular similarity analysis, and the characterization of extended benzenoid systems.
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BibTeX
@article{jantschi2026discrimination,
title = {{Discrimination of Benzenoid Graphs by Topological Polynomials}},
author = {Lorentz Jäntschi},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203777},
url = {https://www.mdpi.com/2227-7390/14/20/3777},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Discrimination of Benzenoid Graphs by Topological Polynomials
AU - Lorentz Jäntschi
PY - 2026
DA - 2026/10/18
JO - Mathematics
DO - 10.3390/math14203777
UR - https://www.mdpi.com/2227-7390/14/20/3777
AB - The discrimination of structural isomers remains a central challenge in mathematical chemistry and molecular graph theory. In this work, twenty topological polynomials are evaluated on benzenoid (polyhex) systems containing between four and seven fused hexagons. Computational analysis of all non-isomorphic benzenoid graphs in this range shows that nine descriptors, including the Theta, Matching, Padmakar–Ivan, Vertex–Szeged, Adjacency Characteristic, Laplacian Characteristic, Signless Laplacian Characteristic, Distance Characteristic, and Harary Matrix Characteristic polynomials, exhibit zero degeneracy and uniquely distinguish all 333 benzenoid isomers with seven hexagons. The structural origin of this behavior is investigated through spectral and distance-based graph properties, and a theoretical framework is proposed distinguishing between (i) computationally verified discrimination on finite sets, (ii) exact algebraic properties and finite-domain completeness for catacondensed benzenoids, and (iii) a composite descriptor completeness conjecture. In contrast, Omega, Sadhana, and Zhang–Zhang polynomials display substantial degeneracy, reflecting information loss associated with quasi-orthogonal cut representations. The obtained results identify a class of topological descriptors with exceptional discriminatory capability and potential applicability in QSAR/QSPR modeling, molecular similarity analysis, and the characterization of extended benzenoid systems.
SN - 2227-7390
ER -