More on linear and metric tree maps

• Autorzy: Kozerenko Sergiy

Identyfikatory

DOI

10.7494/OpMath.2021.41.1.55

• Języki publikacji: EN

Abstrakty

EN

We consider linear and metric self-maps on vertex sets of finite combinatorial trees. Linear maps are maps which preserve intervals between pairs of vertices whereas metric maps are maps which do not increase distances between pairs of vertices. We obtain criteria for a given linear or a metric map to be a positive (negative) under some orientation of the edges in a tree, we characterize trees which admit maps with Markov graphs being paths and prove that the converse of any partial functional digraph is isomorphic to a Markov graph for some suitable map on a tree.

Słowa kluczowe

EN

Markov graph; metric map; non-expanding map; linear map; graph homomorphism

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 1
• Strony: 55--70
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Kozerenko Sergiy

• National University of Kyiv-Mohyla Academy Department of Mathematics, Faculty of Informatics 04070, Skovorody Str. 2, Kyiv, Ukraine

• https://orcid.org/0000-0002-5716-3084

Bibliografia

• [1] H.-J. Bandelt, M. van de Vel, A fixed cube theorem for median graphs, Discrete Math. 67 (1987), 129-137.
• [2] S. Kozerenko, Markov graphs of one-dimensional dynamical systems and their discrete analogues, Rom. J. Math. Comput. Sci. 6 (2016), 16-24.
• [3] S. Kozerenko, Discrete Markov graphs: loops, fixed points and maps preordering, J. Adv. Math. Stud. 9 (2016), 99-109.
• [4] S. Kozerenko, On the abstract properties of Markov graphs for maps on trees, Mat. Bilten 41 (2017), 5-21.
• [5] S. Kozerenko, On disjoint union of M-graphs, Algebra Discrete Math. 24 (2017), 262-273.
• [6] S. Kozerenko, Linear and metric maps on trees via Markov graphs, Comment. Math. Univ. Carolin. 59 (2018), 173-187.
• [7] R. Nowakowski, I. Rival, Fixed-edge theorem for graphs with loops, J. Graph Theory 3 (1979), 339-350.
• [8] R. Nowakowski, I. Rival, On a class of isometric subgraphs of a graph, Combinatorica 2 (1982), 77-88.
• [9] A. Quilliot, A retraction problem in graph theory, Discrete Math. 54 (1985), 61-71.
• [10] E. Wilkeit, Graphs with regular endomorphism monoid, Arch. Math. 66 (1996), 344-352.
• [11] T. Zamfirescu, Non-expanding mappings in graphs, Adv. Appl. Math. Sci. 6 (2010), 23-32.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).