Abstract
Topological indices are important tools for QSPR researches. Wiener, Zagreb, and Randic indices are pioneers of topological indices as the most used topological indices in view of chemistry and chemical graph theory. These three topological indices have been used for modeling physical properties of octanes and other chemical molecules. We firstly define k-total distance degree notion, k-total Zagreb and k-total Randic indices in graph theory. We investigated the prediction power of 3-total Zagreb indices and 3-total Randic index by using some physical properties of octanes such as entropy, acentric factor, enthalpy of vaporizatian and standard enthalpy of vaporization. We showed that these 3-total distance degree based novel indices are possible tools for QSPR studies, which they give a reasonably good correlation greater than 0.92 for modeling acentric factor of octanes. We also showed that 3-total indices give a strong correlation with Wiener index and the second Zagreb index.
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