Local antimagic chromatic number of trees - I. (18th August 2022)

• Record Type: Journal Article
• Authors: Premalatha, K.; Arumugam, S.; Lee, Yi-Chun; Wang, Tao-Ming
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 25:Number 6(2022)
• Page Start: 1591
• Page End: 1602
• Publication Date: 2022-08-18
• Subjects: 05C78 -- 05C69; Antimagic labeling -- Local antimagic labeling -- Local antimagic chromatic number -- Corona of graphs; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2020.1772985
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: Let G = ( V, E ) be a connected graph with | V |= n and | E |= m . A bijection f : E → {1, 2, … , m } is called a local antimagic lableing if for any two adjacent vertices u and v, w ( u ) ≠ w ( v ), where w ( u )= ∑ e ϵ E ( u ) f ( e ) and E ( u ) is the set of edges incident to u . Thus any local antimagic labeling induces a proper vertex coloring of G where the vertex v is assigned the color w ( v ). The local antimagic chromatic number χla ( G ) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G . In this paper we determine the local antimagic chromatic number of several families of trees.