Local Distance Antimagic Labeling of Neighborhood Balanced Graphs

TL;DR

This paper investigates a new type of graph labeling called local distance antimagic labeling, focusing on neighborhood balanced graphs, and explores their chromatic properties and labeling characteristics.

Contribution

It introduces the concept of local distance antimagic labeling for neighborhood balanced graphs and studies their chromatic number and labeling properties.

Findings

Defined local distance antimagic labeling and chromatic number.

Analyzed properties of neighborhood balanced graphs under this labeling.

Provided bounds or exact values for specific classes of graphs.

Abstract

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.