Magic and Antimagic Decomposition of Amalgamation of Cycles

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 = {H_i|1 ≤ i ≤n} such that for every i ≠ j, H_i is isomorphic to H_j, ∪ i=1n H_i = G and should satisfy that E(H_i) ∩ E(H_j) = ∅ if i ≠ j. 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(H_i) = ∑(f(v) + f(e)) = k for v ∈ V(H_i) and e ∈ E(H_i). In this paper, k is called a magic constant. If every subgraph H_i ≅ H and using this labelling results w(H_i) = 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.

Copyright

© 2022 The Authors. Published by Atlantis Press International B.V.

Open Access

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

Download article (PDF)

TY  - CONF
AU  - Sigit Pancahayani
AU  - Annisa Rahmita Soemarsono
AU  - Dieky Adzkiya
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  -