Metric Dimension of Jewel and Jelly _x000C_sh Graphs

Let $G=(V,E)$ be a connected graph and let $d(u,v)$ denote the distance between vertices $u$ and $v$. A subset $W$ of $V(G)$ is called a resolving set for $G$ if for every $u,v\in V(G)$, there exists $w\in W$ such that $d(u, w)\neq d(v, w)$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$ and is denoted by $dim(G)$. \newline The metric dimension has some applications in robotics, because this parameter can represent the minimum number of locations which uniquely determine the position of a robot moving in a graph space. In this paper we compute the metric dimension of the Jewel graph and Jelly fish graph.