Article Version 1 Preserved in Portico This version is not peer-reviewed
Graphs and Binary Systems
Version 1 : Received: 27 June 2018 / Approved: 28 June 2018 / Online: 28 June 2018 (04:48:32 CEST)
A peer-reviewed article of this Preprint also exists.
Kim, H.S.; Neggers, J.; Ahn, S.S. A Method to Identify Simple Graphs by Special Binary Systems. Symmetry 2018, 10, 297. Kim, H.S.; Neggers, J.; Ahn, S.S. A Method to Identify Simple Graphs by Special Binary Systems. Symmetry 2018, 10, 297.
In this paper, we observe that if X is a set and (Bin(X), □) is the semigroup of binary systems on X, then its center ZBin(X) consists of the locally-zero-semigroups and that these can be modeled as (simple) graphs and conversely. Using this device we show that we may obtain many results of interest concerning groupoids by reinterpreting graph theoretical properties and at the same time results on graphs G may be obtained by considering them as elements of centers of the semigroups of binary systems (Bin(X), □) where X = V(G), the vertex set of G.
binary system(groupoid); minimum (mutual) covering set; (mutual) shortest distance; (di)frame graph; d/BCK-algebra
Computer Science and Mathematics, Computer Vision and Graphics
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