| Title:
|
An upper bound of a generalized upper Hamiltonian number of a graph (English) |
| Author:
|
Dzúrik, Martin |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
57 |
| Issue:
|
5 |
| Year:
|
2021 |
| Pages:
|
299-311 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article we study graphs with ordering of vertices, we define a generalization called a pseudoordering, and for a graph $H$ we define the $H$-Hamiltonian number of a graph $G$. We will show that this concept is a generalization of both the Hamiltonian number and the traceable number. We will prove equivalent characteristics of an isomorphism of graphs $G$ and $H$ using $H$-Hamiltonian number of $G$. Furthermore, we will show that for a fixed number of vertices, each path has a maximal upper $H$-Hamiltonian number, which is a generalization of the same claim for upper Hamiltonian numbers and upper traceable numbers. Finally we will show that for every connected graph $H$ only paths have maximal $H$-Hamiltonian number. (English) |
| Keyword:
|
graph |
| Keyword:
|
vertices |
| Keyword:
|
ordering |
| Keyword:
|
pseudoordering |
| Keyword:
|
upper Hamiltonian number |
| Keyword:
|
upper traceable number |
| Keyword:
|
upper H-Hamiltonian number |
| Keyword:
|
Hamiltonian spectra |
| MSC:
|
05C12 |
| MSC:
|
05C45 |
| idZBL:
|
Zbl 07442416 |
| idMR:
|
MR4346115 |
| DOI:
|
10.5817/AM2021-5-299 |
| . |
| Date available:
|
2021-10-06T08:59:51Z |
| Last updated:
|
2022-02-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149135 |
| . |
| Reference:
|
[1] Dzúrik, M.: Metrické vlastnosti grafů.bachelor thesis (2018). |
| Reference:
|
[2] Okamoto, F., Zhang, P.: On upper traceable numbers of graphs.Math. Bohem. 133 (2008), 389–405. MR 2472487, 10.21136/MB.2008.140628 |
| . |
