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

dmtcs:3175 - Discrete Mathematics & Theoretical Computer Science, October 23, 2018, vol. 20 no. 2 - https://doi.org/10.23638/DMTCS-20-2-8
Steiner Distance in Product NetworksArticle

Authors: Yaping Mao ; Eddie Cheng ORCID; Zhao Wang

    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.

    Volume: vol. 20 no. 2
    Section: Graph Theory
    Published on: October 23, 2018
    Accepted on: September 19, 2018
    Submitted on: March 8, 2017
    Keywords: Mathematics - Combinatorics

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