TY - JOUR
T1 - Solis Graphs and Uniquely Metric Basis Graphs
TT -
JF - IJMSI
JO - IJMSI
VL - 17
IS - 2
UR - http://ijmsi.ir/article-1-1442-en.html
Y1 - 2022
SP - 191
EP - 212
KW - Metric dimension
KW - Resolving set
KW - Metric basis
KW - Uniquely metric basis graphs
KW - Solis graph.
N2 - 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.
M3 10.52547/ijmsi.17.2.191
ER -