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Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index

A survey of results and techniques

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Abstract

The Hosoya index and the Merrifield-Simmons index are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure. In recent years, quite a lot of work has been done on the extremal problem for these two indices, i.e., the problem of determining the graphs within certain prescribed classes that maximize or minimize the index value. This survey collects and classifies these results, and also provides some useful auxiliary results, tools and techniques that are frequently used in the study of this type of problem.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa

    Stephan Wagner

  2. Faculty of Science, University of Kragujevac, P.O. Box 60, 34000, Kragujevac, Serbia

    Ivan Gutman

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  1. Stephan Wagner
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Correspondence to Stephan Wagner.

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Wagner, S., Gutman, I. Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index. Acta Appl Math 112, 323–346 (2010). https://doi.org/10.1007/s10440-010-9575-5

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