Magic and Antimagic Decomposition of Amalgamation of Cycles

Authors
Sigit Pancahayani1, *, Annisa Rahmita Soemarsono2, Dieky Adzkiya3, Musyarofah4
1Department of Statistics, Institut Teknologi Kalimantan, Balikpapan, Indonesia
2Department of Mathematics, Institut Teknologi Kalimantan, Balikpapan, Indonesia
3Department of Mathematics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia
4Department of Physics, Institut Teknologi Kalimantan, Balikpapan, Indonesia
*Corresponding author. Email: spancahayani@lecturer.itk.ac.id
Corresponding Author
Sigit Pancahayani
Available Online 8 February 2022.
DOI
10.2991/acsr.k.220202.011How to use a DOI?
Keywords
Amalgamation; Magic; Antimagic; Decomposition; Cycle
Abstract

Consider G = (V, E) as a finite, simple, connected graph with vertex set V and edge set E. G is said to be a decomposable graph if there exists a collection of subgraphs of G, say ℋ = {Hi|1 ≤ in} such that for every ij, Hi is isomorphic to Hj, i=1n Hi = G and should satisfy that E(Hi) ∩ E(Hj) = ∅ if ij. Let f: V(G) ∪ E(G) → {1,2, …, |V(G)| + |E(G)|} be a bijection mapping such that every subgraph in ℋ has the same total of valuation w(Hi) = (f(v) + f(e)) = k for vV(Hi) and eE(Hi). In this paper, k is called a magic constant. If every subgraph HiH and using this labelling results w(Hi) = k for all i, then G admits H-magic decomposition. Otherwise, if the total values among all subgraphs are different, then G admits H-antimagic decomposition. In this research, a graph derived from amalgamating some cycles in a terminal vertex is the object to be investigated to find its property regarding magic decomposition. Furthermore, we find that the vertex amalgamation of some identical cycles admits both magic and antimagic decomposition, which depends on its order.

Open Access
This is an open access article under the CC BY-NC license.

Volume Title
Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
Series
Publication Date
8 February 2022
ISBN
10.2991/acsr.k.220202.011
ISSN
2352-538X
DOI
10.2991/acsr.k.220202.011How to use a DOI?
Open Access
This is an open access article under the CC BY-NC license.

TY  - CONF
AU  - Sigit Pancahayani
AU  - Annisa Rahmita Soemarsono
AU  - Musyarofah
PY  - 2022
DA  - 2022/02/08
TI  - Magic and Antimagic Decomposition of Amalgamation of Cycles
BT  - Proceedings of the  International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021)
PB  - Atlantis Press
SP  - 48
EP  - 52
SN  - 2352-538X
UR  - https://doi.org/10.2991/acsr.k.220202.011
DO  - 10.2991/acsr.k.220202.011
ID  - Pancahayani2022
ER  -