DEGREE-BASED TOPOLOGICAL INDICES IN RANDOM POLYGONAL AND SPIRO CHAINS

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.