An upper bound of a generalized upper Hamiltonian number of a graph

Dzúrik, Martin. "An upper bound of a generalized upper Hamiltonian number of a graph." Archivum Mathematicum 057.5 (2021): 299-311. <http://eudml.org/doc/297516>.

@article{Dzúrik2021,
abstract = {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.},
author = {Dzúrik, Martin},
journal = {Archivum Mathematicum},
keywords = {graph; vertices; ordering; pseudoordering; upper Hamiltonian number; upper traceable number; upper H-Hamiltonian number; Hamiltonian spectra},
language = {eng},
number = {5},
pages = {299-311},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An upper bound of a generalized upper Hamiltonian number of a graph},
url = {http://eudml.org/doc/297516},
volume = {057},
year = {2021},
}

TY - JOUR
AU - Dzúrik, Martin
TI - An upper bound of a generalized upper Hamiltonian number of a graph
JO - Archivum Mathematicum
PY - 2021
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 057
IS - 5
SP - 299
EP - 311
AB - 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.
LA - eng
KW - graph; vertices; ordering; pseudoordering; upper Hamiltonian number; upper traceable number; upper H-Hamiltonian number; Hamiltonian spectra
UR - http://eudml.org/doc/297516
ER -