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...
| Published in: | Mathematics |
|---|---|
| Main Author: | |
| 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 |
| id |
2-s2.0-85214485816 |
|---|---|
| spelling |
2-s2.0-85214485816 Shiu W.-C.; Lau G.-C.; Zhang R. On Bridge Graphs with Local Antimagic Chromatic Number 3 2025 Mathematics 13 1 10.3390/math13010016 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85214485816&doi=10.3390%2fmath13010016&partnerID=40&md5=8304b63ceaca798068c159fed6691c9e 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. Multidisciplinary Digital Publishing Institute (MDPI) 22277390 English Article All Open Access; Gold Open Access; Green Open Access |
| author |
Shiu W.-C.; Lau G.-C.; Zhang R. |
| spellingShingle |
Shiu W.-C.; Lau G.-C.; Zhang R. On Bridge Graphs with Local Antimagic Chromatic Number 3 |
| author_facet |
Shiu W.-C.; Lau G.-C.; Zhang R. |
| author_sort |
Shiu W.-C.; Lau G.-C.; Zhang R. |
| title |
On Bridge Graphs with Local Antimagic Chromatic Number 3 |
| title_short |
On Bridge Graphs with Local Antimagic Chromatic Number 3 |
| title_full |
On Bridge Graphs with Local Antimagic Chromatic Number 3 |
| title_fullStr |
On Bridge Graphs with Local Antimagic Chromatic Number 3 |
| title_full_unstemmed |
On Bridge Graphs with Local Antimagic Chromatic Number 3 |
| title_sort |
On Bridge Graphs with Local Antimagic Chromatic Number 3 |
| publishDate |
2025 |
| container_title |
Mathematics |
| container_volume |
13 |
| container_issue |
1 |
| doi_str_mv |
10.3390/math13010016 |
| url |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85214485816&doi=10.3390%2fmath13010016&partnerID=40&md5=8304b63ceaca798068c159fed6691c9e |
| description |
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. |
| publisher |
Multidisciplinary Digital Publishing Institute (MDPI) |
| issn |
22277390 |
| language |
English |
| format |
Article |
| accesstype |
All Open Access; Gold Open Access; Green Open Access |
| record_format |
scopus |
| collection |
Scopus |
| _version_ |
1823296150811181056 |