2019/05/31 by Modjtaba Ghorbani, Xueliang Li, Ghorbani, Modjtaba +9
Computer Science · Mathematics · #05C05 #05C12 #05C35 #92E10 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #math.CO #msc:05C05 #msc:05C12 #msc:05C35 #msc:92E10
paper · pdf · doi:10.48550/arxiv.1905.13621
12 pages
arxiv created 2019/05/31 · openalex publication_date 2019/05/31 · arxiv updated 2019/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S⊆ V(G), the Steiner distance dG(S) of the set S of vertices in G is the minimum size of a connected subgraph whose vertex set contains or connects S. In this paper, we introduce the concept of the Steiner (revised) Szeged index (rSzk(G)) Szk(G) of a graph G, which is a natural generalization of the well-known (revised) Szeged index of chemical use. We determine the Szk(G) for trees in general. Then we give a formula for computing the Steiner Szeged index of a graph in terms of orbits of automorphism group action on the edge set of the graph. Finally, we give sharp upper and lower bounds of (rSzk(G)) Szk(G) of a connected graph G, and establish some of its properties. Formulas of (rSzk(G)) Szk(G) for small and large k are also given in this paper.