Edge chromatic index and edge-sum chromatic index for families of integral sum graphs

Abstract

We consider class of integral sum graphs $H_{m,j}^{-i,s}$ subject to the conditions $-i<0<s$, $1\le m<i$ and $1\le j<s$ for all $i,s,m,j\in \mathbb{N}$. We apply edge-sum coloring and edge coloring on $H_{m,j}^{-i,s}$. 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 $H_{m,j}^{-i,s}$ 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.