论文信息 - Energy of a polynomial and the Coulson integral formula

Energy of a polynomial and the Coulson integral formula

The energy of an arbitrary polynomial is defined in analogy to the energy of a graph, so that the Coulson integral formula remains valid. In particular, we extend the Coulson integral formula to the case when the zeros of the underlying polynomial are not real and simple. Some related proofs from a recent paper by Peña and Rada are corrected and their results generalized.

[1] C. A. Coulson,et al. On the calculation of the energy in unsaturated hydrocarbon molecules , 1940, Mathematical Proceedings of the Cambridge Philosophical Society.

[2] Anton Betten,et al. Algebraic Combinatorics and Applications : Proceedings , 2001 .

[3] I. Gutman,et al. Maximum energy trees with two maximum degree vertices , 2009 .

[4] I. Gutman,et al. Note on the contribution of a ring to the stability of conjugated molecules , 1984 .

[5] Nenad Trinajstić,et al. Graph theory and molecular orbitals. XV. The Hückel rule , 1976 .

[6] I. Gutman,et al. Mathematical Concepts in Organic Chemistry , 1986 .

[7] Ivan Gutman,et al. Note on the Coulson integral formula , 2006 .

[8] Ernesto Estrada. Spectral theory of networks : from biomolecular to ecological systems , 2009 .

[9] Clemens Heuberger,et al. Chemical trees minimizing energy and Hosoya index , 2009 .

[10] D. Cvetkovic,et al. Spectra of Graphs: Theory and Applications , 1997 .

[11] Ivan Gutman. Acyclic systems with extremal Hückel π-electron energy , 1977 .

[12] B. M. Fulk. MATH , 1992 .

[13] C. Coulson,et al. 591. Conjugation across a single bond , 1949 .

[14] J. Rada,et al. Energy of digraphs , 2008 .