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

Authors:
Stephan Wagner;Ivan Gutman
Affiliations:
Department of Mathematical Sciences, Stellenbosch University, Matieland, South Africa 7602;Faculty of Science, University of Kragujevac, Kragujevac, Serbia 34000
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2010

Citing 18
Cited 4

Another extremal problem for Turan graphs

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Bipartite graphs can have any number of independent sets

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On acyclic systems with minimal Hosoya index

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Extremal double hexagonal chains with respect to k-matchings and k-independent sets

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Maximizing the number of independent subsets over trees with bounded degree

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Trees with m-matchings and the fourth and fifth minimal Hosoya index

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The largest Hosoya index of (n,n+1)-graphs

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Extremal Hosoya index and Merrifield-Simmons index of hexagonal spiders

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Note: On extremal unicyclic molecular graphs with maximal Hosoya index

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Note: Fibonacci numbers and Lucas numbers in graphs

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The number of independent sets in unicyclic graphs with a given diameter

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On the extremal Merrifield-Simmons index and Hosoya index of quasi-tree graphs

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Tricyclic graphs with maximum Merrifield-Simmons index

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The number of independent sets in unicyclic graphs

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The smallest Merrifield-Simmons index of (n,n+1)-graphs

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Minimizing a class of unicyclic graphs by means of Hosoya index

Mathematical and Computer Modelling: An International Journal

On the number of independent sets in cycle-separated tricyclic graphs

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Note: On generalized Fibonacci numbers and k-distance Kp-matchings in graphs

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On the number of independent subsets in trees with restricted degrees

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Energy, Hosoya index and Merrifield-Simmons index of trees with prescribed degree sequence

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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.