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

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On the Strong Rainbow Antimagic Coloring of Some Special Graph

Authors
Wahyu Lestari1, 2, Dafik1, 2, *, Susanto2, Abd. Aziz Wahab3
1PUI-PT Combinatorics and Graph, CGANT, University of Jember, Jember, Indonesia
2Department of Mathematics Education, University of Jember, Jember, Indonesia
3Departement of Islamic Religious Education, Zainul Hasan Genggong, Islamic University, Probolinggo, Indonesia
*Corresponding author. Email: d.dafik@unej.ac.id
Corresponding Author
Dafik
Available Online 27 April 2023.
DOI
10.2991/978-94-6463-138-8_7How to use a DOI?
Keywords
rainbow coloring; strong rainbow; strong rainbow antimagic coloring; connection number
Abstract

Let G(V(G), E(G)) be a connected, undirected, and simple graph with vertex set V(G) and edge set E(G). For a bijective function f : V ( G ) ⟶ { 1 , 2 , . . . , | V ( G ) | } , the associated weight of an edge uvE(G) under f is w ( u v ) = f ( u ) + f ( v ) . The function f is called an edge-antimagic vertex labeling if every edge has distinct weight. For two vertices u and v of G, a u - v geodesic path in G is a u - v path of length d(u, v), where d(u, v) is the distance between u and v (the length of a shortest u - v path in G. A geodesic two edges uv, u ′ v ′ ∈ E ( P ) it satisfied w ( u v ) ≠ w ( u ′ v ′ ) . If for every two vertices u and v of G, there exists a rainbow u - v path, the f is called a strong rainbow antimagic labeling of G. When we assign each edge uv with the color of the edge weight w(uv), thus we say the graph G admits a rainbow antimagic coloring. The strong rainbow antimagic connection number of G, denoted by srac(G), is the smallest number of colors taken over all strong rainbow coloring induced by strong rainbow antimagic labelings of G. In this paper we have determined the connection number of strong rainbow antimagic coloring of some special 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_7How 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  - Wahyu Lestari
AU  - Dafik
AU  - Susanto
AU  - Abd. Aziz Wahab
PY  - 2023
DA  - 2023/04/27
TI  - On the Strong Rainbow Antimagic Coloring of Some Special Graph
BT  - Proceedings of the 6th International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT 2022)
PB  - Atlantis Press
SP  - 61
EP  - 72
SN  - 2352-541X
UR  - https://doi.org/10.2991/978-94-6463-138-8_7
DO  - 10.2991/978-94-6463-138-8_7
ID  - Lestari2023
ER  -