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arXiv · 2406.20032

An Analysis of Graceful Coloring in a Specific r-Regular Graphs

Laavanya D.·Devi Yamini S.
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Abstract

A graceful $l$-coloring of a graph $G$ is a proper vertex coloring with $l$ colors which induces a proper edge coloring with at most $l-1$ colors, where the color for an edge $ab$ is the absolute difference between the colors assigned to the vertices $a$ and $b$. The graceful chromatic number $χ_g(G)$ is the smallest $l$ for which $G$ permits graceful $l$-coloring. The problem of computing the graceful chromatic number of regular graphs is still open, though the existence of the lower bound was proved in \cite{3}. Hence, we pay attention to the computation of the graceful chromatic number of a special class of regular graphs namely complete graphs using set theoretic approach. Also, a few characterization of graphs based on their graceful chromatic number were examined.

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Laavanya D., Devi Yamini S.. 2024-06-28. An Analysis of Graceful Coloring in a Specific r-Regular Graphs. https://arxiv.org/abs/2406.20032

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