%0 Journal Article %A Mohagheghy Nezhad, M. %A Rahbarnia, F. %A Mirzavaziri, M. %A Ghanbari, R. %T Solis Graphs and Uniquely Metric Basis Graphs %J Iranian Journal of Mathematical Sciences and Informatics %V 17 %N 2 %U http://ijmsi.ir/article-1-1442-en.html %R 10.52547/ijmsi.17.2.191 %D 2022 %K Metric dimension, Resolving set, Metric basis, Uniquely metric basis graphs, Solis graph., %X A set $Wsubset V (G)$ is called a resolving set, if for every two distinct vertices $u, v in V (G)$ there exists $win W$ such that $d(u,w) not = d(v,w)$, where $d(x, y)$ is the distance between the vertices $x$ and $y$. A resolving set for $G$ with minimum cardinality is called a metric basis. A graph with a unique metric basis is called a uniquely dimensional graph. In this paper, we establish a family of graph called Solis graph, and we prove that if $G$ is a minimal edge unique base graph with the base of size two, then $G$ belongs to the Solis graphs family. Finally, an algorithm is given for finding the metric dimension of a Solis graph. %> http://ijmsi.ir/article-1-1442-en.pdf %P 191-212 %& 191 %! %9 Research paper %L A-10-3337-1 %+ Department of Applied Mathematics, Ferdowsi University of Mashhad %G eng %@ 1735-4463 %[ 2022