Special Issue "Algebra and Discrete Mathematics"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 November 2019

Special Issue Editor

Guest Editor
Prof. Dr. Seok-Zun Song

Department of Mathematics, Jeju National University, Jeju 63243, Korea
Website 1 | Website 2 | E-Mail
Interests: linear operator; rank preserver; minimum permanents; BCK/BCI-algebras and related systems; fuzzy algebraic structures

Special Issue Information

Dear Colleagues,

Algebra is well-known research subject for almost all mathematicians. It is important to develop computer science and cryptography. In this Special Issue, we hope to communicate new research topics and their applications. In mathematics, BCI/BCK-algebra is an algebraic structure that was introduced by Y. Imai, K. Iséki and S. Tanaka in 1966 to generalize the set difference in set theory, to describe fragments of the propositional calculus involving implications known as BCI and BCK logic. It is known that the class of BCK algebra is a proper subclass of the class of BCI algebra. We refer the reader to useful textbooks on BCI/BCK algebra (see Huang, Y. S. BCI-Algebra. Science Press: Beijing, China, 2006; Iorgulescu, A. Algebras of Logic as BCK Algebras. Editura ASE: Bucharest, Romania, 2008 and Meng J.; Jun, Y.B. BCK-Algebras. Kyung Moon Sa Co.: Seoul, Korea, 1994).

The aim of this Special Issue is to promote the exchange of ideas between researchers and to spread new trends in this area. It is focused on all aspects of algebra and BCK algebra and related algebraic systems from their foundations to applications in computer sciences, informatics and decision-making problems, etc. BCK algebra and related algebraic systems contain MV algebra, BL algebra, R0 algebra, MTL algebra, EQ algebra, lattice implication algebra, equality algebra, hoop algebra, etc.

Prof. Dr. Seok-Zun Song
Guest Editor

Manuscript Submission Information

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Keywords

  • algebra and its applications
  • linear algebra and its applications
  • discrete mathematics
  • BCK-algebras and related algebraic systems
  • (intuitionistic) fuzzy theory and applications
  • soft matrix theory and applications
  • (intuitionistic) fuzzy soft matrix theory and applications
  • neutrosophic soft matrix theory and applications
  • neutrosophic fuzzy matrix theory and applications
  • rough matrix theory and applications 
  • fuzzy soft rough matrix theory and applications

Published Papers (3 papers)

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Research

Open AccessArticle
Neutrosophic Quadruple BCI-Positive Implicative Ideals
Mathematics 2019, 7(5), 385; https://doi.org/10.3390/math7050385
Received: 4 April 2019 / Revised: 20 April 2019 / Accepted: 25 April 2019 / Published: 28 April 2019
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Abstract
By considering an entry (i.e., a number, an idea, an object, etc.) which is represented by a known part (a) and an unknown part (bT,cI,dF) where T,I,F have [...] Read more.
By considering an entry (i.e., a number, an idea, an object, etc.) which is represented by a known part ( a ) and an unknown part ( b T , c I , d F ) where T , I , F have their usual neutrosophic logic meanings and a , b , c , d are real or complex numbers, Smarandache introduced the concept of neutrosophic quadruple numbers. Using the concept of neutrosophic quadruple numbers based on a set, Jun et al. constructed neutrosophic quadruple BCK/BCI-algebras and implicative neutrosophic quadruple BCK-algebras. The notion of a neutrosophic quadruple BCI-positive implicative ideal is introduced, and several properties are dealt with in this article. We establish the relationship between neutrosophic quadruple ideal and neutrosophic quadruple BCI-positive implicative ideal. Given nonempty subsets I and J of a BCI-algebra, conditions for the neutrosophic quadruple ( I , J ) -set to be a neutrosophic quadruple BCI-positive implicative ideal are provided. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics)
Open AccessArticle
Linear Operators That Preserve the Genus of a Graph
Mathematics 2019, 7(4), 312; https://doi.org/10.3390/math7040312
Received: 6 March 2019 / Revised: 21 March 2019 / Accepted: 25 March 2019 / Published: 28 March 2019
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Abstract
A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k1. A mapping of the set of graphs on n vertices to itself [...] Read more.
A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus k 1 . A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of a union of graphs is the union of their images and if it maps the edgeless graph to the edgeless graph. We investigate linear operators on the set of graphs on n vertices that map graphs of genus k to graphs of genus k and graphs of genus k + 1 to graphs of genus k + 1 . We show that such linear operators are necessarily vertex permutations. Similar results with different restrictions on the genus k preserving operators give the same conclusion. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics)
Open AccessArticle
Stanley Depth of Edge Ideals of Some Wheel-Related Graphs
Mathematics 2019, 7(2), 202; https://doi.org/10.3390/math7020202
Received: 28 December 2018 / Revised: 4 February 2019 / Accepted: 6 February 2019 / Published: 21 February 2019
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Abstract
Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In particular, we establish [...] Read more.
Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In particular, we establish general closed formulas for Stanley depth of quotient of edge ideals associated with the m t h -power of a wheel graph, for m 3 , gear graphs and anti-web gear graphs. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics)
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