On number of pendants in local antimagic chromatic number
Publication Date
1-1-2022
Document Type
Article
Publication Title
Journal of Discrete Mathematical Sciences and Cryptography
Volume
25
Issue
8
DOI
10.1080/09720529.2021.1920190
First Page
2673
Last Page
2682
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. Let χ(G) be the chromatic number of G. In this paper, sharp upper and lower bounds of χla (G) for G with pendant vertices, and sufficient conditions for the bounds to equal, are obtained. Consequently, for k ≥ 1, there are infinitely many graphs with k ≥ χ(G) - 1 pendant vertices and χla (G) = k + 1. The work of this paper leads to conjecture and problem on graphs with pendant(s).
Keywords
05C69, 05C78, Local antimagic chromatic number, Local antimagic labeling, Pendant vertices
Department
Mathematics and Statistics
Recommended Citation
Gee Choon Lau, Wai Chee Shiu, and Ho Kuen Ng. "On number of pendants in local antimagic chromatic number" Journal of Discrete Mathematical Sciences and Cryptography (2022): 2673-2682. https://doi.org/10.1080/09720529.2021.1920190