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- W4297800519 abstract "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 $Ssubseteq V(G)$, the emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. Let $n,k$ be two integers with $2leq kleq n$. Then the emph{Steiner $k$-eccentricity $e_k(v)$} of a vertex $v$ of $G$ is defined by $e_k(v)=max {d(S),|,Ssubseteq V(G), |S|=k, and vin S }$. Furthermore, the emph{Steiner $k$-diameter} of $G$ is $sdiam_k(G)=max {e_k(v),|, vin V(G)}$. In 2011, Chartrand, Okamoto and Zhang showed that $k-1leq sdiam_k(G)leq n-1$. In this paper, graphs with $sdiam_4(G)=3,4,n-1$ are characterized, respectively." @default.
- W4297800519 created "2022-10-01" @default.
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- W4297800519 date "2017-02-18" @default.
- W4297800519 modified "2023-09-26" @default.
- W4297800519 title "The Steiner 4-diameter of a graph" @default.
- W4297800519 doi "https://doi.org/10.48550/arxiv.1702.05681" @default.
- W4297800519 hasPublicationYear "2017" @default.
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