@article {
author = {Jannesari, M.},
title = {The metric dimension and girth of graphs},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {41},
number = {3},
pages = {633-638},
year = {2015},
publisher = {Springer and the Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {A set $W\subseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,v\in V(G)$ there exists $w\in W$ such that $d(u,w)\neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $\dim(G)$. In this paper, it is proved that in a connected graph $G$ of order $n$ which has a cycle, $\dim(G)\leq n-g(G)+2$, where $g(G)$ is the length of the shortest cycle in $G$, and the equality holds if and only if $G$ is a cycle, a complete graph or a complete bipartite graph $K_{s,t}$, $ s,t\geq 2$.},
keywords = {Resolving set,metric dimension,girth},
url = {http://bims.iranjournals.ir/article_638.html},
eprint = {http://bims.iranjournals.ir/article_638_d88f00c535acfb7583ac4db47a80194e.pdf}
}