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Chemical Graph Theory
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For a tree, it is equal to the Wiener index. The energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix. Explicit expressions are computed for special graphs, but in general nontrivial integral representations are obtained. An energy index can also be defined based on eigenvalues of the Laplacian matrix and several variants are possible. For example the spectral radius can be used as an invariant, or the Estrada index which is the sum of the exponentials of the eigenvalues.
"Structure vs. Properties Using Chemical Graph Theory" by Tabitha N. Williford
Although the main interest of the text is to introduce all these definitions and properties for applications in molecular chemistry, some of these, especially the spectral and energy indices, have also applications in other domains such as networks. The treatment is however focussing on the theory and the mathematics.
The applications as well as the numerical or algorithmic computations are not included. The book is introductory in the sense that only the main indices are discussed and is restricted to planar graphs, but what is included is worked out in detail. It can be used for a course in mathematical chemistry, or it can be used for self study.
This is a theoretical introduction to the most important indices for molecular graphs. Definitions, properties and proofs for special graphs mainly trees and extremality properties of the indices are derived. Skip to main content. Login Register. Search form Search.
Edge-Wiener Descriptors in Chemical Graph Theory: A Survey
Introduction to Chemical Graph Theory The representation of an atomic structure by a graph where the vertices represent atoms and the edges the bondings, is an important application of connected undirected graphs, studied in a field called chemical graph theory. Combinatorics 92 Biology and other natural sciences, behavioral sciences 92E10 97K3a 05C Shortly afterwards, he moved to South Africa, where he started his career at Stellenbosch University as a lecturer in January His research interests lie mostly in combinatorics and related areas, including connections to other scientific fields such as physics, chemistry and computer science.
His research interests include combinatorics and graph theory, elementary number theory, and related problems.
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