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Theoretical Computer Science and Discrete Mathematics II

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A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (20 February 2023) | Viewed by 2338

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Special Issue Editors

Special Issue Information

Dear Colleagues,

This Special Issue is the continuation of the previous one recently published in Symmetry (https://0-www-mdpi-com.brum.beds.ac.uk/journal/symmetry/special_issues/Computer_Science_Discrete_Mathematics).

The aim of this Special Issue is to attract leading researchers in different areas of discrete mathematics and theoretical computer science. To this end, it is intended to involve in this Special Issue new high-quality results on discrete mathematics including (but not limited to) graph theory, coding theory, cryptography, algorithms and complexity, discrete optimization, discrete geometry, computational geometry, topological indices, molecular descriptors, differential of graphs, metric dimension of graphs, polynomials in graphs, and alliances in graphs. The results on these topics involve their symmetry properties, both from a theoretical and an applied point of view. Contributions presented to the issue can be original research papers, short notes, or surveys.

Dr. Alejandro Estrada-Moreno
Dr. Abel Cabrera Martínez
Guest Editors

Manuscript Submission Information

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. Symmetry 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

graph theory
coding theory
cryptography
algorithms and complexity
discrete optimization
discrete geometry and computational geometry
topological indices and molecular descriptors
differential of graphs
metric dimension of graphs
polynomials and alliances in graphs

Published Papers (2 papers)

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Research

26 pages, 7620 KiB

Open AccessArticle

A New Technique to Uniquely Identify the Edges of a Graph

by Hafiz Muhammad Ikhlaq, Rashad Ismail, Hafiz Muhammad Afzal Siddiqui and Muhammad Faisal Nadeem

Symmetry 2023, 15(3), 762; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15030762 - 20 Mar 2023

Cited by 3 | Viewed by 1455

Abstract

Graphs are useful for analysing the structure models in computer science, operations research, and sociology. The word metric dimension is the basis of the distance function, which has a symmetric property. Moreover, finding the resolving set of a graph is NP-complete, and the possibilities of finding the resolving set are reduced due to the symmetric behaviour of the graph. In this paper, we introduce the idea of the edge-multiset dimension of graphs. A representation of an edge is defined as the multiset of distances between it and the vertices of a set,

B \subseteq V (Γ)

. If the representation of two different edges is unequal, then B is an edge-multiset resolving a set of

Γ

. The least possible cardinality of the edge-multiset resolving a set is referred to as the edge-multiset dimension of

Γ

. This article presents preliminary results, special conditions, and bounds on the edge-multiset dimension of certain graphs. This research provides new insights into structure models in computer science, operations research, and sociology. They could have implications for developing computer algorithms, aircraft scheduling, and species movement between regions. Full article

(This article belongs to the Special Issue Theoretical Computer Science and Discrete Mathematics II)

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13 pages, 2515 KiB

Open AccessArticle

The g-Good-Neighbor Conditional Diagnosability of Exchanged Crossed Cube under the MM* Model

by Xinyang Wang, Haozhe Li, Qiao Sun, Chen Guo, Hu Zhao, Xinyu Wu and Anqi Wang

Symmetry 2022, 14(11), 2376; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14112376 - 10 Nov 2022

Cited by 6 | Viewed by 1039

Abstract

Diagnosability plays an important role in appraising the reliability and fault tolerance of symmetrical multiprocessor systems. The novel g-good-neighbor conditional diagnosability restrains that every fault-free node contains at least g fault-free neighbors and is suitable for large scale multiprocessor systems, attracting a [...] Read more.

M M^{*}

model are separately studied, but only applicable in regular graphs or just ranges rather than exact values. As a promising network structure, in 2019, Guo et al. obtained that the g-good-neighbor diagnosability of the exchanged crossed cube (

E C Q (s, t)

) under the PMC model is

2^{g} (s + 2 - g) - 1

(

t \geq s > g

). We noticed that the exact value of the g-good-neighbor diagnosability of

E C Q (s, t)

under the

M M^{*}

model is still to be determined. In this paper, by proving the upper and lower bounds of the g-good-neighbor diagnosability of

E C Q (s, t)

, for the first time, we derive that the exact value of its g-good-neighbor diagnosability under the

M M^{*}

model is

t_{g}^{m} (E C Q (s, t)) = 2^{g} (s + 2 - g) - 1

(

t \geq s > g

), achieving the unity of the g-good-neighbor diagnosability of ECQ(s, t) under both the PMC model and

M M^{*}

model. Towards the end, simulation experiments are conducted to evaluate the correctness and effectiveness of our conclusion. Our research provides an important supplement to the g-good-neighbor diagnosability of