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Linear Algebra: Matrix Theory, Graph Theory and Applications

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Special Issue Information

Dear Colleagues,

We intend to launch a Special Issue of Axioms. The central topic of this Special Issue will be “Linear Algebra: Matrix Theory, Graph Theory and Applications”. We would like to provide an opportunity to showcase recent developments in both the Matrix Theory and Graph Theory, as well as their applications in different scientific or technological disciplines. In the Keywords section, you will find a list of possible topics, but this list is not exclusive.

We hope to provide a platform to bring together experts, as well as young researchers, in the field to publish original research article.

Prof. Dr. Luis Medina
Guest Editor

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Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Matrix Theory
Vector spaces
Graph Theory
Eigenvalues
Eigenvectors
Inverse eigenvalue problem
Universal realizability
Characteristic polynomial
Permanental polynomials
Energy graph
Estrada index
Spread
Connectivity
Chemical graphs
Graph operation
Line graph
Domination in graphs
Graph matching

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Published Papers (4 papers)

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Research

10 pages, 273 KiB

Open AccessArticle

Higher-Order Jacobsthal–Lucas Quaternions

by Mine Uysal and Engin Özkan

Axioms 2022, 11(12), 671; https://doi.org/10.3390/axioms11120671 - 25 Nov 2022

Cited by 7 | Viewed by 1615

Abstract

In this work, we define higher-order Jacobsthal–Lucas quaternions with the help of higher-order Jacobsthal–Lucas numbers. We examine some identities of higher-order Jacobsthal–Lucas quaternions. We introduce their basic definitions and properties. We give Binet’s formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions, and exponential generating functions of the higher-order Jacobsthal–Lucas quaternions. We also give some relations between higher-order Jacobsthal and Jacobsthal–Lucas quaternions. Full article

(This article belongs to the Special Issue Linear Algebra: Matrix Theory, Graph Theory and Applications)

12 pages, 266 KiB

Open AccessArticle

On Relationships between a Linear Matrix Equation and Its Four Reduced Equations

by Bo Jiang, Yongge Tian and Ruixia Yuan

Axioms 2022, 11(9), 440; https://doi.org/10.3390/axioms11090440 - 30 Aug 2022

Viewed by 1368

Abstract

Given the linear matrix equation

A X B = C

, we partition it into the form [...] Read more.

Given the linear matrix equation

A X B = C

, we partition it into the form

A_{1} X_{11} B_{1} + A_{1} X_{12} B_{2} + A_{2} X_{21} B_{1} + A_{2} X_{22} B_{2} = C

, and then pre- and post-multiply both sides of the equation by the four orthogonal projectors generated from the coefficient matrices

A_{1}

A_{1}

B_{1}

, and

B_{2}

to obtain four reduced linear matrix equations. In this situation, each of the four reduced equations involves just one of the four unknown submatrices

X_{11}

X_{12}

X_{21}

, and

X_{22}

, respectively. In this paper, we study the relationships between the general solution of

A X B = C

and the general solutions of the four reduced equations using some highly selective matrix analysis tools in relation to ranks, ranges, and generalized inverses of matrices. Full article

(This article belongs to the Special Issue Linear Algebra: Matrix Theory, Graph Theory and Applications)

8 pages, 267 KiB

Open AccessArticle

The Eigensharp Property for Unit Graphs Associated with Some Finite Rings

by Heba Adel Abdelkarim, Eman Rawshdeh and Edris Rawashdeh

Axioms 2022, 11(7), 349; https://doi.org/10.3390/axioms11070349 - 20 Jul 2022

Cited by 1 | Viewed by 1476

Abstract

Let R be a commutative ring with unity. The unit graph

G (R)

is defined such that the vertex set of

G (R)

is the set of all elements of R, and two distinct vertices are adjacent if [...] Read more.

Let R be a commutative ring with unity. The unit graph

G (R)

is defined such that the vertex set of

G (R)

is the set of all elements of R, and two distinct vertices are adjacent if their sum is a unit in

R .

In this paper, we show that for each prime,

p, G (Z_{p})

and

G (Z_{2 p})

are eigensharp graphs. Likewise, we show that the unit graph associated with the ring

^{Z_{p} [x]} ∕_{⟨x^{2}⟩}

is an eigensharp graph. Full article

(This article belongs to the Special Issue Linear Algebra: Matrix Theory, Graph Theory and Applications)

10 pages, 810 KiB

Open AccessArticle

Toroidal Spectral Drawing

by Ming-Hsuan Kang and Jing-Wen Gu

Axioms 2022, 11(3), 137; https://doi.org/10.3390/axioms11030137 - 16 Mar 2022

Viewed by 2215

Abstract

We give a deterministic drawing algorithm to draw a graph onto a torus, which is based on the usual spectral drawing algorithm. For most of the well-known toroidal vertex-transitive graphs, the result drawings give an embedding of the graphs onto the torus. Full article

(This article belongs to the Special Issue Linear Algebra: Matrix Theory, Graph Theory and Applications)

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