Abstract

The author surveys his personal contributions to the creation and development of spectral graph theory. Starting from some mathematical problems related to chess in late 1960's, he recognized the relevance of the Perron-Frobenius theory of non-negative matrices and gave an outline of the spectral graph theory in his PhD thesis "Graphs and Their Spectra" in 1971. Since an abbreviated version of the thesis was published in English in a journal, it attracted much attention in scientific circles. Among others, American mathematician Richard Bellman, at that time an editor of Academic Press, proposed to Cvetkovi\' c to publish a monograph on the same subject in his series of books. The resulting monograph "Spectra of Graphs - Theory and Application" was published in 1980 by Academic Press and Deutscher Verlag der Wissenschaften (coauthors M. Doob and H. Sachs). There were a few editions of the book, including a translation into Russian, and it became a standard reference for the field. Related to spectral graph theory, several thousands of scientific papers have been published so far, including those on applications to chemistry, physics and computer science.



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