arXiv subjects

Maurice Genevieva Almeida

Publications and source records attributed to Maurice Genevieva Almeida.

5 recordsLinked to original sources

arXiv2026

Neighborhood Balanced k-Coloring of Graphs

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 each vertex has an equal number of neighbors of each color is called neighborhood-balanced k-coloring, and the graph is called a neighborhood-balanced k-colored graph. This generalizes the notion of neighborhood balanced coloring of graphs introduced by Bryan Freyberg and Alison Marr (Graphs and Combinatorics, 2024). We derive some necessary/sufficient conditions for a graph to admit a neighborhood-balanced k-coloring and discuss several graph classes that admit such colorings. We also show that the problem of determining whether a given graph has such a coloring is NP-complete. Furthermore, we prove that there is no forbidden subgraph characterization for the class of neighborhood-balanced k-colorable graphs.

math.CO↗

arXiv2025

Quasi Neighborhood Balanced Coloring of Graphs

For a simple graph G = (V, E), a coloring of vertices of G using two colors, say red and blue, is called a quasi neighborhood balanced coloring if, for every vertex of the graph, the number of red neighbors and the number of blue neighbors differ by at most one. In addition, there must be at least one vertex in G for which this difference is exactly one. If a graph G admits such a colouring, then G is said to be a quasi-neighbourhood balanced colored graph. We also define variants of such a coloring, like uniform quasi neighborhood balanced coloring, positive quasi neighborhood balanced coloring and negative quasi neighborhood balanced coloring based on the color of the extra neighbor of every vertex of odd degree of the graph G. We present several examples of graph classes that admit the various variants of quasi neighborhood balanced coloring. We also discuss various graph operations involving such graphs. Furthermore, we prove that there is no forbidden subgraph characterization for the class of quasi neighborhood balanced coloring and show that the problem of determining whether a given graph has such a coloring is NP-complete.

math.CO↗

arXiv2025

$(2k+1)$-Neighborhood Balanced Coloring

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.

math.CO↗

arXiv2025

Local Distance Antimagic Labeling of Neighborhood Balanced Graphs

Let G = (V, E) be a graph of order n without isolated vertices. A bijection f from vertex set of G to the set of integers from 1 to n is called a local distance antimagic labeling, if w(u) is not equal to w(v) for every edge uv of G, where w(u) is sum of labels of vertices adjacent to u. The local distance antimagic chromatic number xld(G) is defined to be the minimum number of colors taken over all colorings of G induced by local distance antimagic labelings of G. In this article, we study the local distance antimagic labeling of neighborhood balanced colored graphs.

math.CO↗

arXiv2024

Some Results on Local Distance Antimagic Chromatic Number of Graphs

Let G=(V,E) be a graph of order n without isolated vertices. A bijection f:V -- {1,2,...n} is called a local distance antimagic labeling if the weights of any two adjacent vertices are not equal, where the weight of a vertex is defined to be the sum of labels of adjacent vertices. The local distance antimagic chromatic number is defined to be the minimum number of colors taken over all colorings of G induced by local distance antimagic labelings of G. In this paper, we study the local distance antimagic chromatic number for the join of graphs and the lexicographic product of graphs with empty graphs.

math.CO↗