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The vertex Steiner number of a graph | ||
| Transactions on Combinatorics | ||
| مقاله 30، دوره 9، شماره 2، شهریور 2020، صفحه 115-124 اصل مقاله (509.32 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.116191.1628 | ||
| نویسنده | ||
| J. JOHN* | ||
| Department of Mathematics, Government college of Engineering, Tirunelveli, India- 627007 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Steiner distance؛ Steiner number؛ vertex Steiner number | ||
| مراجع | ||
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