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

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(V, E) 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 (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 χ ′ l e ( 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, 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 (a, d)-edge antimagic chromatic number of some graphs. In this paper we have studied local (a, d)-edge anti-magic coloring on special graphs, namely centipede graphs, lotus graphs, caterpillar graphs, double star graphs, and double broom graphs

Copyright

© 2023 The Author(s)

Open Access

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TY  - CONF
AU  - Eric Dwi Putra
AU  - Dafik
AU  - Arika Indah Kristiana
AU  - Robiatul Adawiyah
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  -