On Local Antimagic Chromatic Number of Cycle-Related Join Graphs

Gee Choon Lau, Wai Chee SHIU, Ho Kuen Ng

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)133-152
Number of pages20
JournalDiscussiones Mathematicae - Graph Theory
Volume41
Issue number1
DOIs
Publication statusPublished - 1 Feb 2021

Scopus Subject Areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

User-Defined Keywords

  • cycle
  • join graphs
  • local antimagic chromatic number
  • Local antimagic labeling

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