Proceedings of the 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)

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On (a, d)-hyperedge Antimagic Labeling of Certain Classes of Hypergraphs: A New Notion

Authors
Dafik1, 2, *, Excelsa Suli Wildhatul Jannah2, Ika Hesti Agustin2, 3, Swaminathan Venkatraman4, Indah Lutfiyatul Mursyidah2, Ridho Alfarisi3, Rafiantika Megahnia Prihandini5
1Department of Postgraduate 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
4Discrete Mathematics Research Laboratory, Srinivasa Ramanujan Centre, SASTRA Deemed University, Thanjavur, India
5Department of Mathematics Education, University of Jember, Jember, Indonesia
*Corresponding author. Email: d.dafik@unej.ac.id
Corresponding Author
Dafik
Available Online 29 June 2024.
DOI
10.2991/978-94-6463-445-7_18How to use a DOI?
Keywords
Hyperedge; antimagic labeling; hypergraph
Abstract

By a hypergraph G , we mean a generalization of a graph G in which an edge can join any number of vertices. In an ordinary graph, an edge connects exactly two vertices, but in hypergraph, an edge or hyperedge may connect more than two vertices. Let G = ( V , E ) be a hypergraph, thus V contains a finite set of vertices, and E contains a hyperedge of subset of V. Some vertices are said to be adjacent if they are elements of a hyperedge. A vertex v is said to be incident to an hyperedge e if v ∈ e . Similarly, a hyperedge e is said to be incident to vertex v if v ∈ e . Furthermore, a bijection f from V ( G ) into { 1 , 2 , 3 , ⋯ , | V | } is called and (a, d)-hyperedge antimagic labeling of hypergraph G if the hyperedge weights W ( e ) = ∑ v ∈ e f ( v ) form an arithmetic progression starting from a and having common difference d. In this paper, we initiate to study hyperedge antimagic labeling of certain classes of hypergraphs, including analyze the properties of the antimagicness of any hypergraph.

Copyright
© 2024 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 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)
Series
Advances in Intelligent Systems Research
Publication Date
29 June 2024
ISBN
10.2991/978-94-6463-445-7_18
ISSN
1951-6851
DOI
10.2991/978-94-6463-445-7_18How to use a DOI?
Copyright
© 2024 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  - Dafik
AU  - Excelsa Suli Wildhatul Jannah
AU  - Ika Hesti Agustin
AU  - Swaminathan Venkatraman
AU  - Indah Lutfiyatul Mursyidah
AU  - Ridho Alfarisi
AU  - Rafiantika Megahnia Prihandini
PY  - 2024
DA  - 2024/06/29
TI  - On (a, d)-hyperedge Antimagic Labeling of Certain Classes of Hypergraphs: A New Notion
BT  - Proceedings of the 2nd International Conference on Neural Networks and Machine Learning 2023 (ICNNML 2023)
PB  - Atlantis Press
SP  - 173
EP  - 183
SN  - 1951-6851
UR  - https://doi.org/10.2991/978-94-6463-445-7_18
DO  - 10.2991/978-94-6463-445-7_18
ID  - 2024
ER  -