KiDM 20160602

Izvor: KiWi

Wiener and anti-Wiener class of indices (Wienerova i anti-Wienerova klasa indeksa)

Abstract: We introduce ordering of tree graphs such that star Sn is minimal, while path Pn is maximal tree. Further, we define a Wiener class of indices so that it consists of topological indices which are increasing on class of trees on n vertices with respect to introduced order and anti-Wiener class of indices so that it consists of decreasing topological indices. Obviously, for any Wiener class index star Sn is minimal, while path Pn is maximal tree, while for any anti-Wiener index path Pn is minimal, while star Sn is maximal tree. Then we introduce a simple criterion on edge contribution function of a topological index which enables us to establish if a topological index belongs to an (anti-)Wiener class. Finally, we apply our result to Wiener index itself and to several generalizations of Wiener index, such as modified Wiener indices, variable Wiener indices and Steiner k-Wiener index.