Steiner k-Eccentric Connectivity Index‎: a Novel Steiner Distance-Based Index

‎Let G be a connected graph and S be a k element subset of the vertex set V(G)‎. ‎The Steiner-k distance d_{G}(S) between vertices of S is the minimum size among all connected subgraphs whose vertex set contains S‎. ‎In this paper‎, ‎we have defined the Steiner k-eccentric connectivity index and derived a closed formula for the same in case of some standard graphs‎. ‎Also‎, ‎we have used Steiner 3-eccentric connectivity index to predict values of boiling point of some primary and secondary amines‎, ‎cross sectional area and molar refraction of alcohols‎. ‎For each‎, ‎regression model is developed and statistical analysis is conducted and these have ensured at least 97\% accuracy‎.