Applicable Analysis and Discrete Mathematics 2023 Volume 17, Issue 1, Pages: 120-137
https://doi.org/10.2298/AADM211211006D
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The structure of the 2-factor transfer digraph common for rectangular, thick cylinder and Moebius strip grid graphs
Đokić Jelena 
(Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia), jelenadjokic@uns.ac.rs
Doroslovački Ksenija (Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia), ksenija@uns.ac.rs
Bodroža-Pantić Olga (Dept. of Math. & Info. Faculty of Science, University of Novi Sad, Serbia), olga.bodroza-pantic@dmi.uns.ac.rs
In this paper, we prove that all but one of the components of the transfer digraph D∗ m needed for the enumeration of 2-factors in the rectangular, thick cylinder and Moebius strip grid graphs of the fixed width m (m ∈ N) are bipartite digraphs and that their orders could be expressed in term of binomial coefficients. In addition, we prove that the set of vertices of each component consists of all the binary m-words for which the difference of numbers of zeros in odd and even positions is constant.
Keywords: 2-factor, Transfer matrix, Thick grid cylinder, Moebius strip
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