Mao, Yaping and Cheng, Eddie and Wang, Zhao - Steiner Distance in Product Networks

dmtcs:3175 - Discrete Mathematics & Theoretical Computer Science, October 23, 2018, vol. 20 no. 2
Steiner Distance in Product Networks

Authors: Mao, Yaping and Cheng, Eddie and Wang, Zhao

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.

Source : oai:arXiv.org:1703.01410
DOI : 10.23638/DMTCS-20-2-8
Volume: vol. 20 no. 2
Section: Graph Theory
Published on: October 23, 2018
Submitted on: March 8, 2017
Keywords: Mathematics - Combinatorics