2018/09/27 by Matjaž Kovše, Kovše, Matjaž, V. A. Rasila +3
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1809.10767
openalex publication_date 2018/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let S be a set of vertices of a connected graph G. The Steiner distance of S is the minimum size of a connected subgraph of G containing all the vertices of S. The sum of all Steiner distances on sets of size k is called the Steiner k-Wiener index, hence for k=2 we get the Wiener index. The modular graphs are graphs in which every three vertices x, y and z have at least one median vertex m(x,y,z) that belongs to shortest paths between each pair of x, y and z. The Steiner 3-Wiener index of a modular graph is expressed in terms of its Wiener index. As a corollary formulae for the Steiner 3-Wiener index of Fibonacci and Lucas cubes are obtained.