Extended Graph Energies in Structure–Property Modeling
Sourav MONDAL, Zahid RAZA
Abstract. Graph-theoretic descriptors are well-known to display molecular topology. The degree-based and graph spectrum-based invariants have attracted considerable attention in chemical graph theory. Here, we investigate numerous graph energies generated from weighted adjacency matrices. We compute these extended energies for a family of benzenoid hydrocarbons and examined in relation to their experimental boiling points. We find from a comparative regression analysis that certain degree-based energies track the variation of boiling point across the series with notable consistency. We observe that incorporating local degree information into the spectral framework enhances sensitivity to changes in ring fusion and molecular growth. Our findings imply that such extended graph energies may serve as practical descriptors in QSPR analysis.
Keywords
Molecular Graph, Graph Energy, Molecular Descriptor, QSPR Analysis
Published online 5/10/2026, 9 pages
Copyright © 2026 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Sourav MONDAL, Zahid RAZA, Extended Graph Energies in Structure–Property Modeling, Materials Research Proceedings, Vol. 66, pp 9-17, 2026
DOI: https://doi.org/10.21741/9781644904152-2
The article was published as article 2 of the book Advanced Materials and Sustainable Energy Technologies
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17-20. https://doi.org/10.1021/ja01193a005
[2] I. Gutman, Degree-Based Topological Indices, Croat. Chem. Acta 86 (2013) 351-361. https://doi.org/10.5562/cca2294
[3] S. Mondal, Z. Raza, Complete solution to open problem on exponential arithmetic-geometric index, Appl. Math. Comput. 513 (2026) 129809. https://doi.org/10.1016/j.amc.2025.129809
[4] Z. Raza, L. Saha, K.C. Das, On inverse symmetric division deg index of graphs, RAIRO Oper. Res. 57 (2023) 3223-3236. https://doi.org/10.1051/ro/2023181
[5] Z. Raza, M. Imran, Expected values of some molecular descriptors in random cyclooctane chains, Symmetry 13 (2021) 2197. https://doi.org/10.3390/sym13112197
[6] Z. Raza, The expected values of some indices in random phenylene chains, The Eur. Phys. J. Plus 136 (2021) 1-15. https://doi.org/10.1140/epjp/s13360-021-01082-y
[7] Z. Raza A. Ali, Bounds on the Zagreb Indices for Molecular (n,m)-Graphs, Int. J. Quantum Chem. 120 (2020) e26333. https://doi.org/10.1002/qua.26333
[8] P. Das, S. Mondal, B. Some, A. Pal, Extension of adjacency matrix in QSPR analysis, Chemom. Intell. Lab. Syst. 243 (2023) 105024. https://doi.org/10.1016/j.chemolab.2023.105024
[9] P. Das, S. Mondal, A. Pal, On Second Zagreb Energy of Graphs, MATCH Commun. Math. Comput. Chem. 92 (2024) 105-131. https://doi.org/10.46793/match.92-1.105D
[10] I. Gutman, B. Furtula, S.B. Bozkurt, On Randic energy, Linear Algebra Appl. 442 (2014) 50-57. https://doi.org/10.1016/j.laa.2013.06.010
[11] S. Mondal, S. Barik, N. De, A. Pal, A note on neighborhood first Zagreb energy and its significance as a molecular descriptor, Chemom. Intell. Lab. Syst. 222 (2022) 104494. https://doi.org/10.1016/j.chemolab.2022.104494
[12] S. Mondal, P. Das, Z. Raza, A. Pal, M. Ghorbani, (2026). Graph Spectrum of Neighbourhood Sombor Matrix and Structure-Property Modelling, Theor. Comput. Sci. 1068 (2026) 115758. https://doi.org/10.1016/j.tcs.2026.115758
[13] I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forsch. Graz 103 (1978) 1-22.

