Trees, unicyclic graphs extremal with respect to Kekule index
The Kekule index of an undirected simple finite graph \(G\) is \(\sum_{\{u,v\}\in E(G)}|d(u)-d(v)|\) where \(d(u)\) is the degree of the vertex \(u\in V(G)\). The Kekule index belongs to a family of topological indices describing properties of graphs that are used for a characterization of chemical and biological activities of molecules modelled by the graph. Let \(\mathcal T_n\) be the family of all trees on an \(n\)-element set. It is proved that the path has the least Kekule index in \(\mathcal T_n\) and the star has the greatest Kekule index in \(\mathcal T_n\). The analogous result is obtained for unicyclic graphs (i.e. a cycle with pendent edges).
scientific article; zbMATH DE number 6356041