A Note Concerning Equipotent Digraph Homomorphism Sets

A Note Concerning Equipotent Digraph Homomorphism Sets

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Author(s)

Author(s): Allen D. Parks

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DOI: 10.18483/ijSci.2017 7 41 47-52 Volume 8 - May 2019

Abstract

Functor adjunctions are fundamental to category theory and have recently found applications in the empirical sciences. In this paper a functor adjunction on a special full subcategory of the category of digraphs is borrowed from mathematical biology and used to equate cardinalities of sets of homomorphisms between various types of digraphs and associated line digraphs. These equalities are especially useful for regular digraphs and are applied to obtain homomorphism set cardinality equalities for the classes of de Bruijn digraphs and Kautz digraphs. Such digraphs play important roles in bioinformatics and serve as architectures for distributed high performance computing networks.

Keywords

Category Theory, Functors, Adjunctions, Digraphs, Line Digraphs, Homomorphisms, De Bruijn Digraphs, Kautz Digraphs

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International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
Author(s) retain the copyrights of this article, though, publication rights are with Alkhaer Publications.

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