Distance magic labelings
| Thesis title in Czech: | Distančně magické očíslování |
|---|---|
| Thesis title in English: | Distance magic labelings |
| Key words: | distančně magické očíslování|Cayleyho graf|hyperkrychle |
| English key words: | distance magic labeling|Cayley graph|hypercube |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Department of Theoretical Computer Science and Mathematical Logic (32-KTIML) |
| Supervisor: | doc. Mgr. Petr Gregor, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 21.09.2022 |
| Date of assignment: | 21.09.2022 |
| Confirmed by Study dept. on: | 07.10.2022 |
| Date and time of defence: | 16.02.2024 09:00 |
| Date of electronic submission: | 18.07.2023 |
| Date of submission of printed version: | 15.01.2024 |
| Date of proceeded defence: | 16.02.2024 |
| Opponents: | RNDr. Ondřej Pangrác, Ph.D. |
| Guidelines |
| A bijective labeling of vertices of a given graph G with numbers from 1 to |V(G)| is D-magic, where D is a set of integers, if the sum of labels of all vertices at distance in D from a vertex v is the same for all vertices v. Recently, there have been several results on D-magic labelings of hypercubes and its several variants that can all be viewed as certain Cayley graphs of the group Z2^n. The goal of the thesis is to unify these results using the means of elementary linear algebra and to obtain new results, possibly for other Cayley graphs or other variants of magic labelings. |
| References |
| [1] P. Anuwiksa, A. Munemasa, R. Simanjuntak, D-Magic and antimagic labelings of hypercubes, ArXiv:1903.05005, 2019, preprint.
[2] S. Arumugam, D. Fronček, and N. Kamatchi, Distance Magic Graphs – A Survey, The Journal of Indonesian Mathematical Society, Special Edition (2011), 11–26. [3] P. Gregor, P. Kovář, Distance magic labelings of hypercubes, Electron. Notes Discrete Math. 40 (2013), 145–149. [4] N. Kang, S. Chen, Z. Li, L. Hou, D-magic labelings of the halved n-cube, Discrete Mathematics 345 (2022), 113044. [5] Š. Miklavič, P. Šparl, On distance magic labelings of Hamming graphs and folded hypercubes, Discuss. Math. Graph Theory, in press. [6] Y. Tian, L. Hou, B. Hou, S. Gao, D-magic labelings of the folded n-cube, Discrete Math. 334 (2021) 112520. |