Publication Date

4-1-2024

Document Type

Article

Publication Title

Iranian Journal of Mathematical Sciences and Informatics

Volume

19

Issue

1

DOI

10.61186/ijmsi.19.1.1

First Page

1

Last Page

17

Abstract

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].

Keywords

Cut-vertices, Local antimagic chromatic number, Local antimagic labeling, Pendants

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

Department

Mathematics and Statistics

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