On Local Antimagic Chromatic Number of Graphs with Cut-vertices

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 Xla(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].