A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION | ||
| Journal of Algebraic Systems | ||
| مقاله 6، دوره 7، شماره 2، فروردین 2020، صفحه 179-187 اصل مقاله (141.75 K) | ||
| نوع مقاله: Research Note | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2019.7367.1363 | ||
| نویسندگان | ||
| M. Mohagheghy Nezhad1؛ F. Rahbarnia* 1؛ M. Mirzavaziri2؛ R. Ghanbari1 | ||
| 1Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran. | ||
| 2Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran. | ||
| چکیده | ||
| The \textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$. In this case, $B$ is called a \textit{metric basis} for $G$. The \textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$. Giving a characterization for those graphs whose metric dimensions are two, we enumerate the number of $n$ vertex metric two dimensional graphs with basic distance 1. | ||
| کلیدواژهها | ||
| Metric dimension؛ Resolving set؛ Metric basis؛ Basic distance؛ Contour of a graph | ||
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