Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)

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On Local (a, d)-Antimagic Coloring of Some Specific Classes of Graphs

Authors
Fadlila Putri Almaidah1, Dafik1, 2, Arika Indah Kristiana1, 2, *, Robiatul Adawiyah1, 2, Rafiantika Megahnia Prihandini1, 2, Ika Hesti Agustin2, 3
1Department of Mathematics Education, University of Jember, Jember, Indonesia
2PUI-PT Combinatorics and Graph, CGANT, University of Jember, Jember, Indonesia
3Department of Mathematics, University of Jember, Jember, Indonesia
*Corresponding author. Email: arika.fkip@unej.ac.id
Corresponding Author
Arika Indah Kristiana
Available Online 27 April 2023.
DOI
10.2991/978-94-6463-138-8_14How to use a DOI?
Keywords
local (a;  d)-antimagic coloring; local edge antimagic coloring; specific graph
Abstract

For any graph G = ( V , E ) , the vertex set V and the edge set E, and let w be the edge weight of graph G, with | V ( G ) | = p and | E ( G ) | = q . A labeling of a graph G is a bijection f from V(G) to the set { 1 , 2 , . . , p } . The bijection f is called an edge antimagic labeling of graph if for any two vertex u and v where w ( u v ) = f ( u ) + f ( v ) , u v ∈ E ( G ) , are distinct. Any local edge antimagic labeling induces a proper edge coloring of G where the edge uv is assigned the color w(uv). The local edge antimagic coloring of graph is said to be a local (a, d)-edge antimagic coloring of G if the set of their edge colors form an arithmetic sequence with initial value a and different d. The local (a, d)-edge antimagic chromatic number X l e ( a , d ) ( G ) is the minimum number of colors needed to color G such that a graph G admits the local (a, d)-edge antimagic coloring. Furthermore, we will obtain the lower and upper bound of X l e ( a , d ) ( G ) . The results of this research are the exact value of the local (a, d)-edge antimagic chromatic number of ladder graph, cycle graph, octopus graph, tadpole graph, tringular book graph, and helm graph.

Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Volume Title
Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
Series
Advances in Physics Research
Publication Date
27 April 2023
ISBN
978-94-6463-138-8
ISSN
2352-541X
DOI
10.2991/978-94-6463-138-8_14How to use a DOI?
Copyright
© 2023 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Fadlila Putri Almaidah
AU  - Dafik
AU  - Arika Indah Kristiana
AU  - Robiatul Adawiyah
AU  - Rafiantika Megahnia Prihandini
AU  - Ika Hesti Agustin
PY  - 2023
DA  - 2023/04/27
TI  - On Local (a, d)-Antimagic Coloring of Some Specific Classes of Graphs
BT  - Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
PB  - Atlantis Press
SP  - 156
EP  - 169
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-138-8_14
DO  - 10.2991/978-94-6463-138-8_14
ID  - Almaidah2023
ER  -