  We consider class of integral sum graphs $H^{-i,s}_{m,j}$ subject to the
conditions $-i<0<s$, $1\leq m < i$ and $1\leq j < s$ for all $i,s, m,j\in
\mathbb{N}$. We apply edge-sum coloring and edge coloring on $H^{-i,s}_{m,j}$.
Since the graphs fully depend on $i$ and $s$, therefore it is not easy to
derive the theoretical as well as numerical results for all values of $i$ and
$s$. Here, we derive the general formula for computing the minimum number of
independent color classes. We compute the edge chromatic as well as edge-sum
chromatic number of $H^{-i,s}_{m,j}$ corresponding to different values of $i$,
$s$, $m$ and $j$. We also compare these two techniques. We place the numerical
results to verify the theoretical results.
