On local distance antimagic chromatic number of graphs disjoint union with 1-regular graphs

• Published in: Proyecciones
• Main Author: Priyadharshini V.; Perrichiappan A.; Nalliah M.; Lau G.-C.
• Format: Article
• Language: English
• Published: Universidad Catolica del Norte 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85201864896&doi=10.22199%2fissn.0717-6279-5963&partnerID=40&md5=0cb31e41c1f07d89f2b6e4b0cfff76ef

Let G be a graph on p vertices and q edges with no isolated vertices. A bijection f: V → {1, 2, 3,.., p} is called local distance antimagic labeling, if for any two adjacent vertices u and v, we have w(u) 6= w(v), where (Formula presented). The local distance antimagic chromatic number χlda(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 paper, we obtained necessary and sufficient condition for the local distance antimagic chromatic number of the disjoint union of some graphs with 1-regular graphs to equal to the number of distinct neighbors of its pendant vertices. We also gave a correct result in [Local Distance Antimagic Vertex Coloring of Graphs, https://arxiv.org/abs/2106.01833v1]. © (2024), (Universidad Catolica del Norte). All rights reserved.