Steiner Distance in Graphs--A Survey

Abstract

For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the \emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. In this paper, we summarize the known results on the Steiner distance parameters, including Steiner distance, Steiner diameter, Steiner center, Steiner median, Steiner interval, Steiner distance hereditary graph, Steiner distance stable graph, average Steiner distance, and Steiner Wiener index. It also contains some conjectures and open problems for further studies.

85 pages, 14 figures, 3 tables

References in corpus (7)

• Community structure in social and biological networks
• Finding and evaluating community structure in networks
• Steiner Distance in Product Networks
• Vertex Decomposition of Steiner Wiener Index and Steiner Betweenness Centrality
• The Steiner 4-diameter of a graph
• The Steiner (n-3)-diameter of a graph
• Steiner 3-diameter, maximum degree and size of a graph

Cited by in corpus (5)

• Steiner Distance in Product Networks
• On the Steiner hyper-Wiener index of a graph
• The Steiner $k$-eccentricity on trees
• On the average Steiner 3-eccentricity of trees
• Wiener index and Steiner 3-Wiener index of a graph