  Let $G$ be a nonempty simple graph with a vertex set $V(G)$ and an edge set
$E(G)$. For every injective vertex labeling $f:V(G)\to\mathbb{Z}$, there are
two induced edge labelings, namely $f^+:E(G)\to\mathbb{Z}$ defined by
$f^+(uv)=f(u)+f(v)$, and $f^-:E(G)\to\mathbb{Z}$ defined by
$f^-(uv)=|f(u)-f(v)|$. The sum index and the difference index are the minimum
cardinalities of the ranges of $f^+$ and $f^-$, respectively. We provide upper
and lower bounds on the sum index and difference index, and determine the sum
index and difference index of various families of graphs. We also provide an
interesting conjecture relating the sum index and the difference index of
graphs.
