Preprint Article Version 1 This version is not peer-reviewed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.

Journal reference: Symmetry 2018, 10, 297
DOI: 10.3390/sym10070297

Abstract

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.

Subject Areas

binary system(groupoid); minimum (mutual) covering set; (mutual) shortest distance; (di)frame graph; d/BCK-algebra

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.