  In this paper we initiate the study of broadcast dimension, a variant of
metric dimension. Let $G$ be a graph with vertex set $V(G)$, and let $d(u,w)$
denote the length of a $u-w$ geodesic in $G$. For $k \ge 1$, let $d_k(x,y)=\min
\{d(x,y), k+1\}$. A function $f: V(G) \rightarrow \mathbb{Z}^+ \cup \{0\}$ is
called a resolving broadcast of $G$ if, for any distinct $x,y \in V(G)$, there
exists a vertex $z \in V(G)$ such that $f(z)=i>0$ and $d_{i}(x,z) \neq
d_{i}(y,z)$. The broadcast dimension, $bdim(G)$, of $G$ is the minimum of
$c_f(G)=\sum_{v \in V(G)} f(v)$ over all resolving broadcasts of $G$, where
$c_f(G)$ can be viewed as the total cost of the transmitters (of various
strength) used in resolving the entire network described by the graph $G$. Note
that $bdim(G)$ reduces to $adim(G)$ (the adjacency dimension of $G$, introduced
by Jannesari and Omoomi in 2012) if the codomain of resolving broadcasts is
restricted to $\{0,1\}$. We determine its value for cycles, paths, and other
families of graphs. We prove that $bdim(G) = \Omega(\log{n})$ for all graphs
$G$ of order $n$, and that the result is sharp up to a constant factor. We show
that $\frac{adim(G)}{bdim(G)}$ and $\frac{bdim(G)}{dim(G)}$ can both be
arbitrarily large, where $dim(G)$ denotes the metric dimension of $G$. We also
examine the effect of vertex deletion on the adjacency dimension and the
broadcast dimension of graphs.
