Computer generation of the characteristic polynomials of chemical graphs

Balasubramanian, K.

doi:10.1002/jcc.540050417

Cited by 77 publications

(40 citation statements)

References 32 publications

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“…Second, graph-theoretical pruning procedures such as the ones described in the present author's papers [30,35] can be employed to simplify the Hamiltonian. The characteristic polynomials of the associated graphs [32] could be very valuable for the generation of properties such as spectral moments, walks on weighted graphs [33], etc. Many important properties of the associated compounds can be generated from the spectral moments.…”

Section: Graph-theoretical Formulation Of the Ppp Methodsmentioning

confidence: 99%

Two colorful applications of the PPP method

Balasubramanian

1990

Int J of Quantum Chemistry

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Two different color-related applications of the Pariser-Pam-Pople method are described. The first one deals with an explanation of the uv-visible absorption spectrum of the curcumin pigment in turmeric and the color change of curcumin upon addition of OH-. The other application deals with blue and red shifts in poly-diacetylene to polybutatriene transformation. The applications of the FEMO and PPP methods to curcumin facilitate assignment of the two observed bands of curcumin (UV and visible) to the r + r* (uv) and n + r* (visible) transitions, respectively. A graph-theoretical formulation of the PPP method is also considered.

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Section: Graph-theoretical Formulation Of the Ppp Methodsmentioning

confidence: 99%

Two colorful applications of the PPP method

Balasubramanian

1990

Int J of Quantum Chemistry

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“…The computer program in Fortran to compute the characteristic polynomials based on the above procedure is described in ref. 4.…”

Section: B Frame's Methods For Computing Characteristic Polynomials Omentioning

confidence: 99%

Computer generation of matching polynimials of chemical graphs and lattices

Ramaraj

Balasubramanian

1985

J Comput Chem

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The resulting polynomials are then assembled to compute the matching polynomial of the initial graph. The program is especially useful in generating the matching polynomials of graphs containing a large number of vertices. The matching polynomials thus generated are potentially useful in several applications such as lattice statistics (dimer covering problem), aromaticity, valence bond methods (enumeration of perfect matchings) in the calculation of grand canonical partition functions, in the computation of thermodynamic properties of saturated hydrocarbons, and in chemical documentation.

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“…Polyene molecules with 8, 9, or 10 carbon vertices can be determined also if one or more eigenvalues are known via embedding or by its alternant or symmetry characteristics (2,3). The method presented in this paper expands the scope of those previously published (4)(5)(6).…”

Section: [L] a 4 = ( 1 / 2 ) ( Q 2 -9 Q + 6 N C ) -2 R 4 -D L -D 4 -3mentioning

confidence: 72%

Facile calculations of select eigenvalues and the characteristic polynomial of small molecular graphs containing heteroatoms

Dias¹

1987

Can. J. Chem.

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JERRY RAY DIAS. 1987. Can. J. Chem. 65, 734 (1987. Determination of common eigenvalues by embedding smaller subgraphs onto larger ones is illustrated. A nearly universal expression of the sixth coefficient of the characteristic polynomial valid for all conjugated hydrocarbon polyenes is presented. Its use in a graph theoretical determination of the Huckel MO characteristic polynomial of molecular graphs possessing heteroatoms is detailed.JERRY RAY DIAS. 1987. Can. J. Chem. 65, 734 (1987 On illustre comment on peut determiner les valeurs propres communes en incorporant des petits graphiques dans des plus grands. On prtsente une expression qui est pratiquement universelle pour la determination du sixi&me coefficient du polynome caracttristique qui est valide pour tous les hydrocarbures polytniques conjugts. On prtsente les details de son utilisation dans la determination, dans la thtorie des graphs, du polyn6me caracttristique des OM de Huckel des graphiques moltculaires posstdant des hettroatomes.[Traduit par la revue]

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Computer generation of the characteristic polynomials of chemical graphs

Cited by 77 publications

References 32 publications

Two colorful applications of the PPP method

Two colorful applications of the PPP method

Computer generation of matching polynimials of chemical graphs and lattices

Facile calculations of select eigenvalues and the characteristic polynomial of small molecular graphs containing heteroatoms

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