Publication Date
2-1-2021
Document Type
Article
Publication Title
Discussiones Mathematicae - Graph Theory
Volume
41
Issue
1
DOI
10.7151/dmgt.2177
First Page
133
Last Page
152
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) = ςf(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, several sufficient conditions for χla(H) ≤ χla(G) are obtained, where H is obtained from G with a certain edge deleted or added. We then determined the exact value of the local antimagic chromatic number of many cycle-related join graphs.
Keywords
cycle, join graphs, local antimagic chromatic number, Local antimagic labeling
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Department
Mathematics and Statistics
Recommended Citation
Gee Choon Lau, Wai Chee Shiu, and Ho Kuen Ng. "On Local Antimagic Chromatic Number of Cycle-Related Join Graphs" Discussiones Mathematicae - Graph Theory (2021): 133-152. https://doi.org/10.7151/dmgt.2177
