On Local Antimagic Chromatic Number of Graphs with Cut-vertices

• Published in: Iranian Journal of Mathematical Sciences and Informatics
• Main Author: Lau G.-C.; Shiu W.-C.; Ng H.-K.
• Format: Article
• Language: English
• Published: Iranian Academic Center for Education, Culture and Research 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85196111343&doi=10.61186%2fijmsi.19.1.1&partnerID=40&md5=110d7bea1b46b9cbe09213324c81f120

An edge labeling of a connected graph G = (V, E) is said to be local antimagic if it is a bijection f: E → {1, …, |E|} such that for any pair of adjacent vertices x and y, f+ (x) ≠ f+ (y), where the induced vertex label f+ (x) =∑ f(e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by χla (G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, the sharp lower bound of the local antimagic chromatic number of a graph with cut-vertices given by pendants is obtained. The exact value of the local antimagic chromatic number of many families of graphs with cut-vertices (possibly given by pendant edges) are also determined. Consequently, we partially answered Problem 3.1 in [Local antimagic vertex coloring of a graph, Graphs and Combin., 33, (2017), 275–285]. © 2024 Academic Center for Education, Culture and Research TMU.