Topological indices are numerical values associated with chemical constitution that are purported to correlate chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful basis for the exploration of proof techniques in discrete mathematics, and its results have applications in many areas of science. One of the useful indices for examining structure-property relationships is the Randic´index. In this study, we present the relationship between the Randic´index, the logarithm of calculated octanol-water partitioning coefficients, and total biodegradation (log K ow and TB d (mol h À1 ), respectively) with the maximum UV wavelength ( max ) and ÁE (ÁE ¼ hc/ max ), as the difference energy level of the HOMO and LUMO orbitals, for the linear simple conjugated polyenes. The results are extended for some of the carotene compounds. The interesting results of relating log K ow , TB d , max , ÁE, and the Randic´index for these compounds are presented.
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