The structure of the 2-factor transfer digraph common for thin cylinder, torus and Klein bottle grid graphs-Reference-Cited by-同舟云学术

The structure of the 2-factor transfer digraph common for thin cylinder, torus and Klein bottle grid graphs

Published:2024 Issue:1 Volume:38 Page:57-65
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Djokic Jelena¹^ORCID,Doroslovacki Ksenija¹^ORCID,Bodroza-Pantic Olga²^ORCID

Affiliation:

1. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

2. Dept. of Math. & Info., Faculty of Science, University of Novi Sad, Novi Sad, Serbia

Abstract

We prove that the transfer digraph D* C,m needed for the enumeration of 2-factors in the thin cylinder TnCm(n), torus TGm(n) and Klein bottle KBm(n) (all grid graphs of the fixed width m and with m?n vertices), when m is odd, has only two components of order 2m?1 which are isomorphic. When m is even, D* C,m has [m/2] + 1 components which orders can be expressed via binomial coefficients and all but one of the components are bipartite digraphs. The proof is based on the application of recently obtained results concerning the related transfer digraph for linear grid graphs (rectangular, thick cylinder and Moebius strip).

Publisher

National Library of Serbia

Reference14 articles.

1. O. Bodroža-Pantić, H. Kwong, R. Doroslovački and M. Pantić, Enumeration of Hamiltonian Cycles on a Thick Grid Cylinder - Part I: Non-contractible Hamiltonian Cycles, Appl. Anal. Discrete Math., 13 (2019), 028-060.

2. O. Bodroža-Pantić, H. Kwong, J. Đokić, R. Doroslovački and M. Pantić, Enumeration of Hamiltonian Cycles on a Thick Grid Cylinder - Part II: Contractible Hamiltonian Cycles, Appl. Anal. Discrete Math., 16 (2022), 246-287.

3. O. Bodroža-Pantić, H. Kwong and M. Pantić, A conjecture on the number of Hamiltonian cycles on thin grid cylinder graphs, Discrete Math. Theor. Comput. Sci. 17:1(2015), 219-240.

4. J. des Cloizeaux, G. Jannik, Polymers in solution: Their modelling and structure, Clarendon Press, Oxford, 1990.

5. J. Đokić, O. Bodroža-Pantić and K. Doroslovački, A spanning union of cycles in rectangular grid graphs, thick grid cylinders and Moebius strips, Trans.Comb. (in press) (2023), http://dx.doi.org/10.22108/toc.2022.131614.1940, extended version (with Appendix) available at http://arxiv.org/abs/2109.12432, (2021), 1-95.