Geodesic
Steiner Distance in Product Networks
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 2.

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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 $S$. Let $n$ and $k$ be two integers with $2\leq k\leq n$. Then the \emph{Steiner $k$-eccentricity $e_k(v)$} of a vertex $v$ of $G$ is defined by $e_k(v)=\max \{d_G(S)\,|\,S\subseteq V(G), \ |S|=k, \ and \ v\in S\}$. Furthermore, the \emph{Steiner $k$-diameter} of $G$ is $sdiam_k(G)=\max \{e_k(v)\,|\, v\in V(G)\}$. In this paper, we investigate the Steiner distance and Steiner $k$-diameter of Cartesian and lexicographical product graphs. Also, we study the Steiner $k$-diameter of some networks. 
@article{DMTCS_2018_20_2_a7,
     author = {Mao, Yaping and Cheng, Eddie and Wang, Zhao},
     title = {Steiner {Distance} in {Product} {Networks}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2018},
     doi = {10.23638/DMTCS-20-2-8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-2-8/}
}
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Mao, Yaping; Cheng, Eddie; Wang, Zhao. Steiner Distance in Product Networks. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 2. doi : 10.23638/DMTCS-20-2-8. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-2-8/

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