On Bridge Graphs with Local Antimagic Chromatic Number 3

Let (Formula presented.) be a connected graph. A bijection (Formula presented.) is called a local antimagic labeling if, for any two adjacent vertices x and y, (Formula presented.), where (Formula presented.), and (Formula presented.) is the set of edges incident to x. Thus, a local antimagic labeli...

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Bibliographic Details
Published in:Mathematics
Main Author: Shiu W.-C.; Lau G.-C.; Zhang R.
Format: Article
Language:English
Published: Multidisciplinary Digital Publishing Institute (MDPI) 2025
Online Access:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85214485816&doi=10.3390%2fmath13010016&partnerID=40&md5=8304b63ceaca798068c159fed6691c9e
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Summary:Let (Formula presented.) be a connected graph. A bijection (Formula presented.) is called a local antimagic labeling if, for any two adjacent vertices x and y, (Formula presented.), where (Formula presented.), and (Formula presented.) 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 (Formula presented.). The local antimagic chromatic number (Formula presented.) 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 (Formula presented.) and give several ways to construct bridge graphs with (Formula presented.). © 2024 by the authors.
ISSN:22277390
DOI:10.3390/math13010016