Closed Neighborhood Balanced k-Coloring of Graphs

Fuente: arXiv
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Autori principali: Almeida, Maurice, Pawar, Ravindra, Gupta, Siddharth, Singh, Tarkeshwar
Natura: Preprint
Pubblicazione: 2025
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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