Publication details
An upper bound of a generalized upper Hamiltonian number of a graph
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | Archivum Mathematicum |
| MU Faculty or unit | |
| Citation | |
| web | http://dx.doi.org/10.5817/AM2021-5-299 |
| Doi | http://dx.doi.org/10.5817/AM2021-5-299 |
| Keywords | graph; vertices; ordering; pseudoordering; upper Hamiltonian number; upper traceable number; upper H-Hamiltonian number; Hamiltonian spectra |
| Description | 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. |