Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs. Benzenoid Hydrocarbons

The spectral moments of the edge adjacency matrix recently have been successfully employed in quantitative structure−property relationship (QSPR) and quantitative structure−activity relationship (QSAR) studies of alkanes, alkyl halides, benzyl alcohols, and cycloalkanes.1-3 In this work we examined spectral moments of the edge adjacency matrix of benzenoid hydrocarbons. We designed combinatorial formulas for spectral moments up to the seventh order. Our expressions depend on counts of certain structural features that can easily be deduced from the molecular graph. The first few spectral moments of the edge adjacency matrix and of the vertex adjacency matrix depend on the very same structural parameters, implying that the two sets of moments are equivalent from the vewpoint of QSPR and QSAR studies. We demonstrate this for the total π-electron energy.

[1]  Jerry Ray Dias.  A periodic table for polycyclic aromatic hydrocarbons: Part X. On the characteristic polynomial and other structural invariants [1] , 1987 .

[2]  N. Trinajstic.  Chemical Graph Theory , 1992 .

[3]  J. Burdett,et al.  Moments method and elemental structures , 1985 .

[5]  G. G. Hall.  The bond orders of alternant hydrocarbon molecules , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[6]  G. G. Hall,et al.  Effect of Bay Regions on the Total π-Electron Energy of Benzenoid Hydrocarbons , 1992 .

[7]  Ernesto Estrada,et al.  Spectral Moments of the Edge-Adjacency Matrix of Molecular Graphs, 2. Molecules Containing Heteroatoms and QSAR Applications , 1997, J. Chem. Inf. Comput. Sci..

[8]  J. Ciosłowski.  Upper Bound for Total π-Electron Energy of Benzenoid Hydrocarbons , 1985 .

[9]  Ante Graovac,et al.  On a resonance energy model based on expansion in terms of acyclic moments: Exact results , 1991 .

[10]  Stephen Lee,et al.  Second-moment scaling and covalent crystal structures , 1991 .

[11]  Ernesto Estrada,et al.  Topological Indices Based on the Line Graph of the Molecular Graph , 1996, J. Chem. Inf. Comput. Sci..

[12]  Ivan Gutman,et al.  Remark on the moment expansion of total π-electron energy , 1992 .

[13]  S. J. Cyvin,et al.  Introduction to the theory of benzenoid hydrocarbons , 1989 .

[14]  Svetlana Marković,et al.  The evaluation of spectral moments for molecular graphs of phenylenes , 1997 .

[15]  A graphical evaluation of characteristic polynomials of huckel trees , 1986 .

[16]  Jerry Ray Dias.  Facile calculations of select eigenvalues and the characteristic polynomial of small molecular graphs containing heteroatoms , 1987 .

[17]  Ernesto Estrada,et al.  A Topological Index Based on Distances of Edges of Molecular Graphs , 1996, J. Chem. Inf. Comput. Sci..

[18]  Rudolph A. Marcus,et al.  Additivity of Heats of Combustion, LCAO Resonance Energies, and Bond Orders of Conformal Sets of Conjugated Compounds , 1965 .

[19]  Ernesto Estrada,et al.  Edge Adjacency Relationships and a Novel Topological Index Related to Molecular Volume , 1995, J. Chem. Inf. Comput. Sci..

[20]  Ivan Gutman,et al.  Dependence of spectral moments of benzenoid hydrocarbons on molecular structure , 1991 .

[21]  Rudolph A. Marcus,et al.  On the Theory of Chemiluminescent Electron‐Transfer Reactions , 1965 .

[22]  Yuansheng Jiang,et al.  Evaluation of moments and their application in Hückel molecular orbital theory , 1984 .

[23]  Jeremy K. Burdett,et al.  Moments and the energies of solids , 1985 .

[24]  George G. Hall.  The evaluation of moments for polycyclic hydrocarbons , 1986 .

[25]  Ernesto Estrada,et al.  Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs, 1. Definition and Applications to the Prediction of Physical Properties of Alkanes , 1996, J. Chem. Inf. Comput. Sci..

[26]  Ernesto Estrada,et al.  Edge adjacency relationships in molecular graphs containing heteroatoms: a new topological index related to molar volume , 1995, J. Chem. Inf. Comput. Sci..

[27]  Yuansheng Jiang,et al.  Stability and reactivities based on moment analysis , 1989 .

[28]  S. Markovic,et al.  The evaluation of the eighth moment for benzenoid graphs , 1992 .

[29]  Ivan Gutman,et al.  Spectral moments of polymer graphs , 1996 .

[30]  Ernesto Estrada,et al.  Spectral Moments of the Edge Adjacency Matrix in Molecular Graphs. 3. Molecules Containing Cycles , 1998, J. Chem. Inf. Comput. Sci..