%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