Closed Neighborhood Balanced k-Coloring of Graphs
Combinatorics
2025-10-21 v1
Abstract
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.
Cite
@article{arxiv.2510.16666,
title = {Closed Neighborhood Balanced k-Coloring of Graphs},
author = {Maurice Almeida and Ravindra Pawar and Siddharth Gupta and Tarkeshwar Singh},
journal= {arXiv preprint arXiv:2510.16666},
year = {2025}
}