Address: Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
E-mail: 451859@mail.muni.cz
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.
AMSclassification: primary 05C12; secondary 05C45.
Keywords: graph, vertices, ordering, pseudoordering, upper Hamiltonian number, upper traceable number, upper H-Hamiltonian number, Hamiltonian spectra.
DOI: 10.5817/AM2021-5-299