An Analysis of Graceful Coloring in a Specific r-Regular Graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917708266733568 |
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| author | D., Laavanya S., Devi Yamini |
| author_facet | D., Laavanya S., Devi Yamini |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_20032 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Analysis of Graceful Coloring in a Specific r-Regular Graphs D., Laavanya S., Devi Yamini Combinatorics 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. |
| title | An Analysis of Graceful Coloring in a Specific r-Regular Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.20032 |