AU - Mohagheghy Nezhad, M.
AU - Rahbarnia, F.
AU - Mirzavaziri, M.
AU - Ghanbari, R.
TI - Solis Graphs and Uniquely Metric Basis Graphs
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 17
VI - 2
IP - 2
4099 - http://ijmsi.ir/article-1-1442-en.html
4100 - http://ijmsi.ir/article-1-1442-en.pdf
SO - IJMSI 2
ABĀ - 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.
CP - IRAN
IN - Department of Applied Mathematics, Ferdowsi University of Mashhad
LG - eng
PB - IJMSI
PG - 191
PT - Research paper
YR - 2022