Eccentric connectivity index of the non-commuting graph associated to the Dihedral groups of order at most 12 / Zulfazleen Natasha Zulkiflee and Nur Idayu Alimon

A topological index is a numerical value or invariant in mathematics that characterizes specific topological aspects of a space, manifold, or mathematical object. Topological indices are used to differentiate between topological spaces or to capture specific characteristics of their structure. Meanwhile, a non-commuting graph is a graph in which two unique vertices are adjacent if, and only if, they do not commute, meaning xy≠yx and it consists of the non-central elements set in a group as a vertex. In this paper, since there are lack of connecting the topological indices and the graphs related to finite groups, the eccentric connectivity index (ECI) of the non-commuting graph for certain order of dihedral groups, is computed. As a result, the eccentric connectivity index of non-commuting graphs for dihedral groups increases as the order of the groups increases. In real life, one of the eccentric connectivity index's effects is that it can be utilized as a chemical descriptor in drug discovery to predict biological activities such as binding affinities to target proteins or enzymes.