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...
| Published in: | MATHEMATICS |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI
2025
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| Subjects: | |
| Online Access: | https://www-webofscience-com.uitm.idm.oclc.org/wos/woscc/full-record/WOS:001393709500001 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |
| DOI: | 10.3390/math13010016 |