On symmetric division deg index of unicyclic graphs and bicyclic graphs with given matching number

Nowadays, it is an important task to find extremal values on any molecular descriptor with respect to different graph parameters. In a molecular graph, the vertices represent the atoms and the edges represent the chemical bonds in the terms of graph theory. For one thing, the molecular graphs of som...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 8; pp. 9020 - 9035
Main Authors Sun, Xiaoling, Gao, Yubin, Du, Jianwei
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
bicyclic graph
matching number
perfect matching
symmetric division deg index
unicyclic graph
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Summary:Nowadays, it is an important task to find extremal values on any molecular descriptor with respect to different graph parameters. In a molecular graph, the vertices represent the atoms and the edges represent the chemical bonds in the terms of graph theory. For one thing, the molecular graphs of some chemical compounds are unicyclic graphs or bicyclic graphs, such as benzene compounds, napthalene, cycloalkane, et al. For another, the symmetric division deg index is proven to be a potentially useful molecular descriptor in quantitative structure-property/activity relationships (QSPR/QSAR) studies recently. Therefore, we present the maximum symmetric division deg indices of unicyclic graphs and bicyclic graphs with given matching number. Furthermore, we identify the corresponding extremal graphs.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021523