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Book Review: Dušanka Janežič, Ante Miličević, Sonja Nikolić, and Nenad Trinajstić, Graph-Theoretical Matrices in Chemistry

Croatian Chemical Society
Publication Date
  • Design
  • Mathematics


books.vp BOOK REVIEWS Du{anka Jane`i}, Ante Mili~evi}, Sonja Nikoli}, and Nenad Trinajsti} Graph-Theoretical Matrices in Chemistry Mathematical Chemistry Monographs, No. 3, Ed. I. Gutman University of Kragujevac and Faculty of Science, Kragujevac, Kragujevac (Serbia), 2007, pp. 205 ISBN 978-86-81829-72-1 (hard cover) There are a few graphical representations of molecular structure (constitution) and hundreds of topological indi- ces. However, to derive a topological index from a mo- lecular graph, the first step is to construct its matrix, or to say it more explicitly, every molecular index rests on a graph-theoretical matrix. Thus, the third book in the series Mathematical Chemistry Monographs is devoted exclusively to matrices used in topological analysis of molecules. The book generally deals with adjacency, incidence, and distance matrices. As every graph consists of verti- ces (V) and edges (E), there are, according to the second classification, two kinds of matrices, i.e., vertex- and edge-matrices. But these are very crude classifications; the book describes a total of 130 matrices, i.e., 17 kinds of adjacency matrices, 6 kinds of incidence matrices, 28 kinds of distance (»and related») matrices, and 18 kinds of »special matrices» (Wiener matrices, reverse Wiener matrices, Szeged matrices, Cluj matrices, Hosoya ma- trix, path matrix, etc.). Chapter 6 of the book is devoted to graphical matrices, and shows how to derive topologi- cal indices from them. Altogether, in its seven chapters (Introduction, The Adjacency Matrix and Related Matrices, Incidence Ma- trices, Distance Matrices and Related Matrices, Special Matrices, Graphical Matrices, and Concluding Remarks), 72 paragraphs, 205 pages, and 365 references, followed by the well designed Subject index, this small book gives to informed as well as to not-so-well informed readers a short, compact, and systematic overview over all kinds of matrices derived by

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