On Bridge Graphs with Local Antimagic Chromatic Number 3

Wai-Chee Shiu, Gee-Choon Lau and Ruixue Zhang ()
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Wai-Chee Shiu: Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Gee-Choon Lau: College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, Johor Branch, Segamat Campus, Johor 85000, Malaysia
Ruixue Zhang: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China

Mathematics, 2024, vol. 13, issue 1, 1-17

Abstract: Let G = ( V , E ) be a connected graph. A bijection f : E → { 1 , … , | E | } is called a local antimagic labeling if, for any two adjacent vertices x and y , f + ( x ) ≠ f + ( y ) , where f + ( x ) = ∑ e ∈ E ( x ) f ( e ) , and E ( x ) is the set of edges incident to x . Thus, a local antimagic labeling induces a proper vertex coloring of G , where the vertex x is assigned the color f + ( x ) . The local antimagic chromatic number χ l a ( G ) is the minimum number of colors taken over all colorings induced by local antimagic labelings of G . In this paper, we present some families of bridge graphs with χ l a ( G ) = 3 and give several ways to construct bridge graphs with χ l a ( G ) = 3 .

Keywords: local antimagic labeling; local antimagic chromatic number; s -bridge graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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