On Bridge Graphs with Local Antimagic Chromatic Number 3

Let G=(V,E) be a connected graph. A bijection f:E ->{1,& mldr;,|E|} is called a local antimagic labeling if, for any two adjacent vertices x and y, f+(x)not equal f+(y), where f+(x)=& sum;e is an element of E(x)f(e), and E(x) is the set of edges incident to x. Thus, a local antimagic labe...

全面介绍

书目详细资料
发表在:MATHEMATICS
Main Authors: Shiu, Wai-Chee; Lau, Gee-Choon; Zhang, Ruixue
格式: 文件
语言:English
出版: MDPI 2025
主题:
在线阅读:https://www-webofscience-com.uitm.idm.oclc.org/wos/woscc/full-record/WOS:001393709500001
实物特征
总结:Let G=(V,E) be a connected graph. A bijection f:E ->{1,& mldr;,|E|} is called a local antimagic labeling if, for any two adjacent vertices x and y, f+(x)not equal f+(y), where f+(x)=& sum;e is an element of 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 chi la(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 chi la(G)=3 and give several ways to construct bridge graphs with chi la(G)=3.
ISSN:
2227-7390
DOI:10.3390/math13010016