Description
Speaker: Matjaz Kovse, LaBRI, France
Title: Vertex Decomposition of Steiner Wiener Index and Steiner Betweenness Centrality
ABSTRACT. The Steiner diversity is a type of multi-way metric measuring the size of a Steiner tree between vertices of a graph and it generalizes the geodetic distance. The Steiner Wiener index is the sum of all Steiner diversities in a graph and it generalizes the Wiener index. Recently the Steiner Wiener index has found an interesting application in chemical graph theory as a molecular structure descriptor composed of increments representing interactions between sets of atoms, based on the concept of the Steiner diversity. Amon other results a formula based on a vertex contributions of the Steiner Wiener index by a newly introduced Steiner betweenness centrality, which measures the number of Steiner trees that include a particular vertex as a non-terminal vertex, will be presented. This generalizes Krekovski and Gutman's Vertex version of the Wiener Theorem and a result of Gago on the average betweenness centrality and the average distance in general graphs.