Antimagic labelings of a complete graph
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915350013018112 |
|---|---|
| author | Bhavale, Dr A. N. |
| author_facet | Bhavale, Dr A. N. |
| contents | In $1990$, Hartsfield and Ringel introduced antimagic graphs. Hartsfield and Ringel conjectured that every connected graph (and in particular, a tree) except $K_2$ is antimagic. In $2010$, Hefetz et al.\ raised two questions: Is every orientation of any simple connected undirected graph antimagic? and Given any undirected graph $G$, does there exist an orientation of $G$ which is antimagic? They call such an orientation an {\it antimagic orientation} of $G$. Recently, Bhavale provided an edge labeling for a given graph on $n$ vertices without isolated vertices. In this paper, using the labeling of Bhavale, we prove that a complete graph $K_n$ for $n \geq 3$ is super antimagic as well as totally antimagic total graph. We also prove that there exists an antimagic orientation of $K_n$ for $n \geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Antimagic labelings of a complete graph Bhavale, Dr A. N. Combinatorics 05C78 In $1990$, Hartsfield and Ringel introduced antimagic graphs. Hartsfield and Ringel conjectured that every connected graph (and in particular, a tree) except $K_2$ is antimagic. In $2010$, Hefetz et al.\ raised two questions: Is every orientation of any simple connected undirected graph antimagic? and Given any undirected graph $G$, does there exist an orientation of $G$ which is antimagic? They call such an orientation an {\it antimagic orientation} of $G$. Recently, Bhavale provided an edge labeling for a given graph on $n$ vertices without isolated vertices. In this paper, using the labeling of Bhavale, we prove that a complete graph $K_n$ for $n \geq 3$ is super antimagic as well as totally antimagic total graph. We also prove that there exists an antimagic orientation of $K_n$ for $n \geq 3$. |
| title | Antimagic labelings of a complete graph |
| topic | Combinatorics 05C78 |
| url | https://arxiv.org/abs/2506.15221 |