TY - JOUR
ID - 24580
TI - The vertex Steiner number of a graph
JO - Transactions on Combinatorics
JA - TOC
LA - en
SN - 2251-8657
AU - JOHN, J.
AD - Department of Mathematics, Government college of Engineering, Tirunelveli, India- 627007
Y1 - 2020
PY - 2020
VL - 9
IS - 2
SP - 115
EP - 124
KW - Steiner distance
KW - Steiner number
KW - vertex Steiner number
DO - 10.22108/toc.2020.116191.1628
N2 - 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 G if $W \cup \lbrace x \rbrace$ is a Steiner set of G. The minimum cardinality of an $x$-Steiner set of G is defined as $x$-Steiner number of G and denoted by $s_x(G)$. Some general properties satisfied by these concepts are studied. The $x$-Steiner numbers of certain classes of graphs are determined. Connected graphs of order p with $x$-Steiner number 1 or $p-1$ are characterized. It is shown that for every pair a, b of integers with $2 \leq a \leq b$, there exists a connected graph G such that $s(G)} = a$ and $s_{x}(G)=b$ for some vertex $x$ in G, where $s(G)$ is the Steiner number of a graph.
UR - https://toc.ui.ac.ir/article_24580.html
L1 - https://toc.ui.ac.ir/article_24580_0d5028a2912e9c2fbf79c364b27d26e3.pdf
ER -