2017/02/19 by Zhao Wang, Yaping Mao, Wang, Zhao +5 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1702.05681
openalex publication_date 2017/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Steiner distance of a graph, introduced by Chartrand, Oellermann, Tian and Zou 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) among the vertices of S is the minimum size among all connected subgraphs whose vertex sets contain S. Let n,k be two integers with 2≤ k≤ n. Then the Steiner k-eccentricity ek(v) of a vertex v of G is defined by ek(v)=max \d(S) | S⊆ V(G), |S|=k, and v∈ S \. Furthermore, the Steiner k-diameter of G is sdiamk(G)=max \ek(v) | v∈ V(G)\. In 2011, Chartrand, Okamoto and Zhang showed that k-1≤ sdiamk(G)≤ n-1. In this paper, graphs with sdiam4(G)=3,4,n-1 are characterized, respectively.