RT - Journal Article
T1 - On Local Antimagic Chromatic Number of Graphs with Cut-vertices
JF - IJMSI
YR - 2024
JO - IJMSI
VO - 19
IS - 1
UR - http://ijmsi.ir/article-1-1726-en.html
SP - 1
EP - 17
K1 - Local antimagic labeling
K1 - Local antimagic chromatic number
K1 - Cut-vertices
K1 - Pendants.
AB - 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].
LA eng
UL http://ijmsi.ir/article-1-1726-en.html
M3 10.61186/ijmsi.19.1.1
ER -