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arXiv · 2303.04762

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

Priyanka B R·Biswajit Pandit·Rajeswari M
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Abstract

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.

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Priyanka B R, Biswajit Pandit, Rajeswari M. 2023-03-08. Edge chromatic index and edge-sum chromatic index for families of integral sum graphs. https://arxiv.org/abs/2303.04762

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