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Metric dimension of lexicographic product of some known graphs | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 1 - شماره پیاپی 26، بهمن 2023، صفحه 269-277 اصل مقاله (523.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.20814.1384 | ||
| نویسنده | ||
| Mohsen Jannesari* | ||
| Department of Science, Shahreza Campus, University of Isfahan, Iran | ||
| چکیده | ||
| For an ordered set $W=\{w_1,w_2,\ldots,w_k\}$ of vertices and a vertex $v$ in a connected graph $G$, the ordered $k$-vector $r(v|W):=(d(v,w_1),d(v,w_2),\ldots,d(v,w_k))$ is called the (metric) representation of $v$ with respect to $W$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The set $W$ is called a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. The minimum cardinality of a resolving set for $G$ is its metric dimension. In this paper, we investigate the metric dimension of the lexicographic product of graphs $G$ and $H$, $G[H]$, for some known graphs. | ||
| کلیدواژه‌ها | ||
| Lexicographic product؛ Resolving set؛ Metric dimension؛ Basis؛ Adjacency dimension | ||
| مراجع | ||
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