Local Distance Antimagic Labeling of Neighborhood Balanced Graphs

2025/05/13 by Almeida, Maurice Genevieva
#05C 78 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.08134

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.

Citations

• Local Antimagic Coloring of Some Graphs
• On join product and local antimagic chromatic number of regular graphs
• Local Distance Antimagic Vertex Coloring of Graphs
• On a combination of the 1-2-3 Conjecture and the Antimagic Labelling Conjecture
• A Dynamic Survey of Graph Labeling

Related

• Local Distance Antimagic Vertex Coloring of Graphs
• Some Results on Local Distance Antimagic Chromatic Number of Graphs
• Affirmative Solutions On Local Antimagic Chromatic Number
• Local antimagic chromatic number of partite graphs
• On local antimagic chromatic number of cycle-related join graphs II