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

# 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 (ad)-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 (ad)-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 (ad)-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 (ad)-edge antimagic chromatic number of ladder graph, cycle graph, octopus graph, tadpole graph, tringular book graph, and helm graph.

Open Access

Volume Title
Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
Series
Publication Date
27 April 2023
ISBN
10.2991/978-94-6463-138-8_14
ISSN
2352-541X
DOI
10.2991/978-94-6463-138-8_14How to use a DOI?
Open Access

TY  - CONF
AU  - Dafik
AU  - Arika Indah Kristiana
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  -