On Local Antimagic Chromatic Number of Graphs with Cut-vertices
Gee-Choon Lau, Wai Chee Shiu, Ho-Kuen Ng · Iranian Journal of Mathematical Sciences and Informatics · 2024
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 χ la (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