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The Total π-Electron Energy Saga

Ivan Gutman orcid id ; Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia
Boris Furtula ; Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Serbia

Puni tekst: engleski pdf 4.118 Kb

str. 359-368

preuzimanja: 1.919



The total π-electron energy, as calculated within the Hückel tight-binding molecular orbital approximation, is a quantum-theoretical characteristic of conjugated molecules that has been conceived as early as in the 1930s. In 1978, a minor modification of the definition of total π-electron energy was put forward, that made this quantity interesting and attractive to mathematical investigations. The concept of graph energy, introduced in 1978, became an extensively studied graph-theoretical topic, with many hundreds of published papers. A great variety of graph energies is being considered in the current mathematical-chemistry and mathematical literature. Recently, some unexpected applications of these graph energies were discovered, in biology, medicine, and image processing.
We provide historic, bibliographic, and statistical data on the research on total π-electron energy and graph energies, and outline its present state of art. The goal of this survey is to provide, for the first time, an as-complete-as-possible list of various existing variants of graph energy, and thus help the readers to avoid getting lost in the jungle of references on this topic.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Ključne riječi

total π-electron energy; graph energy; molecular graph; chemical graph theory; spectral graph theory

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