Closed Neighborhood Balanced k-Coloring of Graphs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912659376439296 |
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| author | Almeida, Maurice Pawar, Ravindra Gupta, Siddharth Singh, Tarkeshwar |
| author_facet | Almeida, Maurice Pawar, Ravindra Gupta, Siddharth Singh, Tarkeshwar |
| contents | For a simple graph G = (V, E) and a positive integer k greater than or equal to 2, a coloring of vertices of G using exactly k colors such that every vertex has an equal number of vertices of each color in its closed neighborhood is called closed neighborhood-balanced k-coloring, and the graph which admits such a coloring is called closed neighborhood balanced k-colored graph. We derive some necessary/sufficient conditions for a graph to admit a closed neighborhood balanced k-coloring and discuss various graph operations involving such graphs. Furthermore, we prove that there is no forbidden subgraph characterization for the class of closed neighborhood-balanced k-colorable graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Closed Neighborhood Balanced k-Coloring of Graphs Almeida, Maurice Pawar, Ravindra Gupta, Siddharth Singh, Tarkeshwar Combinatorics 05C 15 05C 78 For a simple graph G = (V, E) and a positive integer k greater than or equal to 2, a coloring of vertices of G using exactly k colors such that every vertex has an equal number of vertices of each color in its closed neighborhood is called closed neighborhood-balanced k-coloring, and the graph which admits such a coloring is called closed neighborhood balanced k-colored graph. We derive some necessary/sufficient conditions for a graph to admit a closed neighborhood balanced k-coloring and discuss various graph operations involving such graphs. Furthermore, we prove that there is no forbidden subgraph characterization for the class of closed neighborhood-balanced k-colorable graphs. |
| title | Closed Neighborhood Balanced k-Coloring of Graphs |
| topic | Combinatorics 05C 15 05C 78 |
| url | https://arxiv.org/abs/2510.16666 |