Abstract

A topological descriptors is a numerical quantity associated with the chemical structures which play an essential role in the chemical graph theory. In this work, we state and prove the expected values of the degree- based topological indices and generalized $ ISI_{(\alpha, \beta)} $ index for the random $ l $-polygonal chain and random $ l $-polygonal spiro chain. Based on the results above, we present the average values of the $ TIs $ with respect to the set of all polygonal and spiro polygonal chains with $ n $ polygons. As applications, we apply the affiliated formulae to obtain the expected values of the $ TIs $ of some special polygonal chains and spiro polygonal chains. Furthermore, we present diverse representations of graph that highlights the correlations between expected mean of indices and structural parameters.

Keywords and Phrases

Topological indices, Generalized ISI index, Random polygonal chain, Random polygonal spiro chain, Expected value, Average value.

A.M.S. subject classification

05C09, 05C80, 05C90, 05C92.

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