$(2k+1)$-Neighborhood Balanced Coloring
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908525140115456 |
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| author | Almeida, Maurice Genevieva |
| author_facet | Almeida, Maurice Genevieva |
| contents | Let $G=(V,E)$ be a simple graph and $(2k+1)$ be a prime integer. Let each vertex of $G$ be colored using one of the $(2k+1)$ colors, say $R_1,R_2,...,R_{2k+1}$. If every vertex has an equal number of neighbors of each color, then the coloring is a $(2k+1)$-neighborhood balanced coloring. We establish a number of results for common families of graphs and present some families of graphs that have this property. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_07758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $(2k+1)$-Neighborhood Balanced Coloring Almeida, Maurice Genevieva Combinatorics 05C 78 Let $G=(V,E)$ be a simple graph and $(2k+1)$ be a prime integer. Let each vertex of $G$ be colored using one of the $(2k+1)$ colors, say $R_1,R_2,...,R_{2k+1}$. If every vertex has an equal number of neighbors of each color, then the coloring is a $(2k+1)$-neighborhood balanced coloring. We establish a number of results for common families of graphs and present some families of graphs that have this property. |
| title | $(2k+1)$-Neighborhood Balanced Coloring |
| topic | Combinatorics 05C 78 |
| url | https://arxiv.org/abs/2505.07758 |