A study of the Quantity of Matchings in Some Classes of Graphs

Student: Nikita Kuzmin

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Data Mining (Master)

Year of Graduation: 2024

When searching for graphs with extreme values of the Hosoya index, a number of standard techniques are usually used. Among these techniques, we note the proof of the absence of hanging vertices by standard graph transformations, establishing the form of the resulting graphs, their parameterization and parameter tuning using standard cycle splittings and rolling cycles along a path or cycle using the properties of Fibonacci numbers. This paper proposes a new method for searching for graphs from given classes that have the maximum z-index value, based on special local transformations.

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