(2k+1)-Neighborhood Balanced Coloring

2025/05/12 by Maurice Genevieva Almeida, Almeida, Maurice Genevieva
Computer Science · Mathematics · #05C 78 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2505.07758

openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 R₁,R₂,...,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.

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