Compatible Adjacency Relations for Digital Products
Abstract
The present paper studies several types of compatible adjacency relations for digital products such as a $C$-compatible adjacency (or the $L_C$-property in \cite{H13}), an $S$-compatible adjacency in \cite{H19} (or the $L_S$-property in \cite{H13}), which can contribute to the study of product properties of digital spaces (or digital images).
Furthermore, to study an automorphism group of a Cartesian product of two digital coverings which do not satisfy a radius $2$ local isomorphism, which remains open,
the paper uses some properties of an ultra regular covering in \cite{H16}. By using this approach, we can substantially classify digital products.
In particular, using a $C$-compatible adjacency (or the $L_C$-property), we address a product problem of a digital isomorphism (see Theorems 3.6 and 4.1).
Furthermore, to study an automorphism group of a Cartesian product of two digital coverings which do not satisfy a radius $2$ local isomorphism, which remains open,
the paper uses some properties of an ultra regular covering in \cite{H16}. By using this approach, we can substantially classify digital products.
In particular, using a $C$-compatible adjacency (or the $L_C$-property), we address a product problem of a digital isomorphism (see Theorems 3.6 and 4.1).
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