Publication details

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



Year of publication 2021
Type Article in Periodical
Magazine / Source Archivum Mathematicum
MU Faculty or unit

Faculty of Science

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.

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