Wiener index of graphs with radius two
Summary: The Wiener index of a graph is the sum of the distances between all pairs of vertices. It has been one of main descriptors that correlate a chemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics. We characterize graphs with the maximum Wiener index among all graphs of order \(n\) with radius two. In addition, we pose a conjecture concerning the minimum Wiener index of graphs with given radius. If this conjecture is true, it will be able to answer an open question by \textit{Z. You} and \textit{B. Liu} [MATCH Commun. Math. Comput. Chem. 66, No. 1, 343--344 (2011; Zbl 1264.05040)].
scientific article; zbMATH DE number 6169815
scientific article