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

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

Authors
Eric Dwi Putra1, Dafik2, 3, Arika Indah Kristiana2, 3, *, Robiatul Adawiyah2, 4, Rafiantika Megahnia Prihandini2
1Department of Mathematics Education, University of PGRI Argopuro Jember, Jember, Indonesia
2PUI-PT Combinatorics and Graph, CGANT, University of Jember, Jember, Indonesia
3Department of Postgraduate Mathematics Education, University of Jember, Jember, Indonesia
4Department of Mathematics Education, 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_5How to use a DOI?
Keywords
local ( a , d ) $$(a , d)$$ antimagic coloring; edge antimagic coloring; spacial graph
Abstract

For any graph G = ( V , E ) , the order and size of G are p and q. Let G(VE) be a graph with the vertex set V and the edge set E, and let w be the edge weight of graph G. with | V ( G ) | = m and | E ( G ) | = n . A labeling of a graph G is a bijection f from V(G) to the set { 1 , 2 , . . , p | V ( G ) | } . The bijection f is called an edge antimagic labeling of graph if for any two vertex u and v in path u - v , u v , where { w ( u v ) : w ( u v ) = f ( u ) + f ( v ) , u v E } , 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 χ l e ( G ) is the minimum number of colors needed to color G such that a graph G admits the local (ad)-edge antimagic coloring. Furthermore, In this paper, we will obtain the lower and upper bound of χ l e ( G ) . The results of this research are the exact value of the local (ad)-edge antimagic chromatic number of some graphs. In this paper we have studied local (ad)-edge anti-magic coloring on special graphs, namely centipede graphs, lotus graphs, caterpillar graphs, double star graphs, and double broom graphs

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
978-94-6463-138-8
ISSN
2352-541X
DOI
10.2991/978-94-6463-138-8_5How to use a DOI?
Open Access

TY  - CONF
AU  - Eric Dwi Putra
AU  - Dafik
AU  - Arika Indah Kristiana
AU  - Rafiantika Megahnia Prihandini
PY  - 2023
DA  - 2023/04/27
TI  - On Local (a, d)-Edge 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  - 42
EP  - 53
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-138-8_5
DO  - 10.2991/978-94-6463-138-8_5
ID  - Putra2023
ER  -