@article {
author = {JOHN, J},
title = {The vertex steiner number of a graph},
journal = {Transactions on Combinatorics},
volume = {9},
number = {2},
pages = {115-124},
year = {2020},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2020.116191.1628},
abstract = {Let $x$ be a vertex of a connected graph $G$ and $W \subset V(G)$ such that $x\notin W$. Then $W$ is called an $x$-Steiner set of \textit{G} if $W \cup \lbrace x \rbrace$ is a Steiner set of \textit{G}. The minimum cardinality of an $x$-\textit{Steiner set} of \textit{G} is defined as $x$-\textit{Steiner number} of \textit{G} and denoted by $s_x(G)$. Some general properties satisfied by these concepts are studied. The $x$-\textit{Steiner numbers} of certain classes of graphs are determined. Connected graphs of order \textit{p} with $x$-Steiner number 1 or $p-1$ are characterized. It is shown that for every pair \textit{a}, \textit{b} of integers with $2 \leq a \leq b$, there exists a connected graph \textit{G} such that $s(G)} = a$ and $s_{x}(G)=b$ for some vertex $x$ in \textit{G}, where $s(G)$ is the \textit{Steiner number} of a graph.},
keywords = {Steiner distance,Steiner number,vertex Steiner number},
url = {https://toc.ui.ac.ir/article_24580.html},
eprint = {https://toc.ui.ac.ir/article_24580_0d5028a2912e9c2fbf79c364b27d26e3.pdf}
}