Some Results on Local Distance Antimagic Chromatic Number of Graphs*

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Goa, India

2 Rosary College of Commerce and Arts, Navelim, Salcete-Goa, India

Abstract

Let G = (V,E) be a simple graph of order n without isolated vertices. A bijection f : V →{1,2,...,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 the sum of the labels of neighbors of vertex u. The local distance antimagic chromatic number of a graph χld(G) is defined as the minimum number of colors taken over all the colorings of G induced by local distance antimagic labeling 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 the complement of the complete graph.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 26 June 2026

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