Complete solutions on local antimagic chromatic number of three families of disconnected graphs

• Published in: COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION
• Main Authors: Chan, Tsz Lung; Lau, Gee-Choon; Shiu, Wai Chee
• Format: Article; Early Access
• Language: English
• Published: AZARBAIJAN SHAHID MADANI UNIV 2024
• Subjects: Mathematics
• Online Access: https://www-webofscience-com.uitm.idm.oclc.org/wos/woscc/full-record/WOS:001186635800001

An edge labeling of a 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) =6 f+(y), where the induced vertex label f+(x) = E f (e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by chi la(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, we study local antimagic labeling of disjoint unions of stars, paths and cycles whose components need not be identical. Consequently, we completely determined the local antimagic chromatic numbers of disjoint union of two stars, paths, and 2-regular graphs with at most one odd order component respectively.