We describe the Italy-South Africa Research Program 2018–2020, focusing on the mobility scheme “Algebraic Graph Theory and Complex Networks” which supported a series of scientific initiatives between the University of Cape Town (Cape Town, South Africa) and the University of Naples Federico II (Naples, Italy) during the years 2018–2021. We sketch the relevant steps of the collaboration, focusing on the creation of a network of researchers between Italy and South Africa in the fields of Graph Theory and Combinatorics. In this context it becomes more relevant the role of the “Workshop on Graphs, Topology and Topological Groups 2021” and of the corresponding proceedings

Belardo F.

Russo F. G.

Sarti P.

English

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http://toc.ui.ac.irTransactions on CombinatoricsISSN (print): 2251-8657, ISSN (on-line): 2251-8665Vol. 11 No. 3 (2022), pp. i-viii.© 2022 University of Isfahanwww.ui.ac.irINTRODUCTION TO THE PROCEEDINGS OF WGTTG2021FRANCESCO BELARDO, FRANCESCO G. RUSSO∗ AND PIERGUIDO SARTIAbstract. We describe the Italy-South Africa Research Program 2018–2020, focusing on the mobil-ity scheme “Algebraic Graph Theory and Complex Networks” which supported a series of scientificinitiatives between the University of Cape Town (Cape Town, South Africa) and the University ofNaples Federico II (Naples, Italy) during the years 2018–2021. We sketch the relevant steps of thecollaboration, focusing on the creation of a network of researchers between Italy and South Africa inthe fields of Graph Theory and Combinatorics. In this context it becomes more relevant the role of the“Workshop on Graphs, Topology and Topological Groups 2021” and of the corresponding proceedings.1. A brief description of ISARP 2018–2020South Africa and Italy have a long lasting bilateral partnership in science and technology. TheItaly-South Africa Research Programme (ISARP) is implemented and funded by the Italian Ministryof Foreign Affairs and International Cooperation (MAECI) and the National Research Foundationof the South African Department of Science and Innovation within the framework of the Scientificand Technological Cooperation Agreement between the Government of the Republic of Italy and theGovernment of the Republic of South Africa, signed in Pretoria on 15 January, 1998 and entered intoforce on 19 February, 2000.ISARP aims to facilitate the development of sustainable institutional links between the two coun-tries. The overall aim of this Programme is not only to build on existing, outstanding and establishedresearch partnerships but to also foster new linkages and engagements with small cohorts of youngand emerging researchers for new links between South Africa and Italy. The selection process is basedon scientific soundness, excellence being an essential criteria from both countries.A new call for proposals is going to be jointly issued in the coming months by the South African Na-tional Research Foundation and MAECI - Directorate General for Cultural and Economic Promotionand Innovation – Office IX.Manuscript Type: Workshop on Graphs, Topology and Topological Groups (Cape Town, South Africa).∗Corresponding author.iii Trans. Comb. 11 no. 3 (2022) i-viii F. Belardo, F. G. Russo and P. Sarti• Successful mobility ProjectsSA-ITA executive programmeShaping future S&T cooperation: 2018-2020No Thematic Area Title Italian PI South African PI 1New Technologies for Social ScienceA spatial and social investigation at the Moxomatsi village,Mpumalanga (SSIMM)Dr. S. BARBAUniSADr. E. NKAMBULETshwane University of Technology, Pretoria2Green Energy Optimal power distribution from renewable energy resourcesDr. S. RUGGERIUniCADr. D. OYEDOKUNUniversity of Cape Town  3Green Energy Synthesis and characterization of innovative materials with bothmultiferroic and photovoltaic propertiesDr. D. DEL MONTECNRDr. VV. SRINIVASUUniversity Johannesburg4Green Energy BIO-waste-to-ENERGYDr. FAVAROUniPDDr. R. CRIPWELL Stellenbosch University5Green EnergyEvaluation of novel metal-organic framework composites for biogaspurificationDr. A. LANZINIPolitenico TODr. R. OBOIRIENCSIR - Materials Science and Manufacturing_Pretoria6Green EnergyCarbon emissions reduction and climate change protection throughzero waste.Dr. D. SPIGAUniCA Dr. D. TROISUniversity of KwaZulu-Natal7 ICT Algebraic Graph Theory and Complex NetworksDr. BELARDOUniNA Dr. F. RUSSOUniversity of Cape Town 8  Green EnergyNovel High Temperature Zr based nano-structured coatings forselective solar absorbers for Concentration Solar Power applications Dr. B. SOTILLO BUZARRACNRDr. L. KOTSEDI(NANOAFNET), iThemba LABS, NationalResearch Foundation, Western Cape Figure 1. Successful projects of mobility schemes within ISARP 2018–2020.The latest call for proposals was issued in 2017, inviting applications from South African and Italianpartnering research institutions for two funding schemes, one to support Joint Research Projects (JRP)- aimed at promoting collaborative projects with clearly defined goals - and one to facilitate ResearchStaff Exchange – where only costs related to travel are funded (see Figure 1).The cooperation areas span a wide range of sectors in the applied and theoretical sciences andtechnology. The list is periodically revised to align the areas of cooperation to emerging sectors ofmutual interest and opportunity.Multilateral or bilateral funding programs - like ISARP, the network of Science and TechnologyAttachés – which has been greatly expanded in the last two years, and the Trieste Science Hub areimportant parts of the Italian science diplomacy tools.Science and technology represent a composite sector profoundly linked to areas of cooperation suchas research and trade. Researchers, entrepreneurs and institutions now have new modern tools to easethe access regarding the Italian science and technology system and its opportunities. The MAECI,in collaboration with the Ministry of University and Research, has created the platform Innovitalia:https://innovitalia.esteri.it/, which aims at offering those who work in the research and inno-vation system, both in Italy and abroad, constant updates on the actions of Italian scientific diplomacyand on opportunities for bilateral and multilateral scientific and technological cooperation. The portalintends to enhance the network of Italian researchers abroad (see e.g. Figure 2 for an idea of the dis-tribution in scientific sectors of the Italian researchers in South Africa), offering a space for networkingiiTrans. Comb. 11 no. 3 (2022) i-viii F. Belardo, F. G. Russo and P. Sarti iiiNetwork of Italian Researchers at the Cape (NIRC) https://nircblog.wordpress.com/Figure 2. Presence of Italian researchers in the Western Cape in 2021.and collaboration between the various actors of Italian research and innovation on the internationalscene, sharing information on research, work and specialization opportunities in different countries.The proceedings of the “ Workshop on Graphs, Topology and Topological Groups” WGTTG2021,and the corresponding volume of contributions in the “Transactions on Combinatorics”, should beinterpreted as the final product of a scientific program between Italy and South Africa, designed tocooperate on topics of Spectral Graph Theory, Compex Networks and Combinatorics. These threefields are indeed relevant for the formation of young academics in South Africa, but they are also threefields which can contribute to the creation of a scientific network of long term.2. The scientific initiatives of “Algebraic Graph Theory and Complex Networks”Since WGTTG2021 is a part of ISARP 2018–2020, we should mention that WGTTG2021 wassupported by the National Research Foundation of South Africa (NRF) and by the Ministero deli AffariEsteri e della Cooperazione Internazionale of Italy (MAECI), but these two institutions supported infact the whole project “Algebraic Graph Theory and Complex Networks” within ISARP 2018–2020.We are going to mention briefly the main steps of the collaboration during the years 2018–2021.The first moment of interaction between the principal investigators of “Algebraic Graph Theoryand Complex Networks” goes back to the meetingWorkshop on Algebraic Graph Theory and Complex Networksiiiiv Trans. Comb. 11 no. 3 (2022) i-viii F. Belardo, F. G. Russo and P. SartiFigure 3. Workshop on Algebraic Graph Theory and Complex Networks in September2018 (Naples, Italy).University of Naples Federico IINaples, Italy, 13th and 14th of September 2018http://www.dma.unina.it/ocsuser/ocs/index.php/WAGTCN/2018This meeting held in person and it allowed young South African researchers to travel, putting themin contact with experts in the fields of Spectral Graph Theory and Combinatorics.From the motivation, the people involved, the energies and the level of the scientific talks of thismeeting, it was clear that the mutual interactions would have been of benefit both for the research unitof the Italian principal investigator and for the research unit of the South African principal invesigator,namelyTopology, Algebra and Dynamical SystemsUniversity of Cape Townhttps://sites.google.com/site/topolalgeb/homeSince the group of research “Topology, Algebra and Dynamical Systems” had some young post-graduate students, who were interested to acquire knowledge in combinatorics, there was the chanceto have a series of lectures of advanced level one year later. The lectures dealt with Spectral GraphTheory and were presented within the periodic activities of the research group in Cape Town, namelyCourse for PhD and MSc studentsSpectral Graph Theory of Signed GraphsivTrans. Comb. 11 no. 3 (2022) i-viii F. Belardo, F. G. Russo and P. Sarti vFigure 4. A PhD course on Spectral Graph Theory at University of Cape Town duringthe month of December 2019.University of Cape Town, 13/16/17/18/19 December 2019https://drive.google.com/file/d/15SoJRL4TaLCdhd_7h0_mXUvn825m15R0/viewOf course, the lectures were face-to-face and this was another important moment of collaboration,where it was possible to share ideas and perspectives in algebraic combinatorics.The last step was supposed to happen in March 2020, but there were restrictions due to covid19, andthese restrictions changed deeply the social behaviours during the years 2020 and 2021. In particularit has changed the usual tradition to do research in person via meetings and workshops. Thereforethe original plans, regarding the realization of the “ Workshop on Graphs, Topology and TopologicalGroups”, were modified and the meeting was postponed and it held online in March 2021, due to apersisting situation of uncertainty for travels and mobility.Despite the difficulties due to covid19 restrictions, the energy of the people involved, the presenceof the institutions and the motivation both from the Italian part and the South African part wereintensive, in fact WGTTG2021 was successful. This meeting had a large number of participants,offering a forum of scientific discussion between the national experts in the area of graph theory bothin Italy and in South Africa, but saw also participants from Nigeria, Spain, Germany, Turkey, Iran,Serbia, USA, Sweden, Ethiopia, Namibia. We mention the main links of WGTTG2021 below:Workshop on Graphs, Topology and Topological Groups 2021 [Online]University of Cape Town, Cape Town, South Africa10th of March 2021, Zoom Meetingvvi Trans. Comb. 11 no. 3 (2022) i-viii F. Belardo, F. G. Russo and P. SartiFigure 5. WGTTG2021 [Online] in March 2021 (Cape Town, South Africa).https://sites.google.com/site/topolalgeb/home/conferences/wgttg-2021-onlineIt should be mentioned the additional activity of formation for young academics, developed as aparallel event of WGTTG2021. This was a course of advanced level, which touched a sensitive topicof research such as the geometric group theory. Our warmest thanks go to Prof. Enric Ventura (Uni-versitat Politècnica de Catalunya, Barcelona, Spain) who gave this course and offered his experienceand availability to the participants of WGTTG2021. It represented another significant opportunity ofgrowth for the young South African academics involved in the project:Course for PhD and MSc studentsStallings Graphs and the Lattice of Subgroups of Free GroupsUniversity of Cape Town, 8/9/11/12 March 2021https://drive.google.com/file/d/16rg45oWv-daqextax7lCLFZJO_NTSZMF/viewThe publication of the proceedings of WGTTG2021 is the concrete and permanent trace of the wholecollaboration. We should thank explicitly Prof. Alireza Abdollahi (University of Isfahan, Isfahan,Iran), since he gave the availability to publish the contributions of our meeting in the “Transactionson Combinatorics”. The result is a volume of very fine quality, whose authors and titles appear below:viTrans. Comb. 11 no. 3 (2022) i-viii F. Belardo, F. G. Russo and P. Sarti viiAuthors: Y. BavumaTitle: A short note on the decomposition of the central product of groups——————————————————–Authors: F. Belardo and M. BrunettiTitle: On eigenspaces of some compound complex unit gain graphs——————————————————–Authors: M. Cavaleri, A. Donno and D. D’AngeliTitle: On the characteristic polynomial and spectrum of Basilica Schreier graphs——————————————————–Authors: J. Delgado and E. VenturaTitle: A list of applications of Stallings automata——————————————————–Authors: H.P. Künzi and F. YildizTitle: A directed graph associated with a T0-quasi-metric space——————————————————–Authors: V.R. Misanantenaina and S. WagnerTitle: A polynomial associated with rooted trees and specific posets——————————————————–Authors: S.K. MuhieTitle: Spectral properties of the non-permutability graph of subgroups——————————————————–Last but not least, we should thank the participants of WGTTG2021, the referees who carefullychecked the contributions in these proceedings, the Italian Embassy of Pretoria (Pretoria, SouthAfrica), the Italian Consulate of Cape Town (Cape Town, South Africa) for the constant support,the National Research Foundation of South Africa (Pretoria, South Africa), the University of CapeTown (Cape Town, South Africa), the University of Naples Federico II (Naples, Italy), the GNFM ofInDAM (Florence, Italy), the GNSAGA of InDAM (Florence, Italy).Francesco BelardoDipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, Via Cintia,Complesso Universitario Monte S. Angelo, I-80126 , Naples, ItalyEmail: fbelardo@gmail.comviiviii Trans. Comb. 11 no. 3 (2022) i-viii F. Belardo, F. G. Russo and P. SartiFrancesco G. RussoDepartment of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X1, 7701, RondeboschCape Town, South AfricaandDepartment of Mathematics and Applied Mathematics, University of the Western Cape, New CAMS Building, PrivateBag X17, 7535, Bellville, South AfricaEmail: francescog.russo@yahoo.comPierguido SartiMinistero degli Affari Esteri e della Cooperazione Internazionale, Ambasciata d’Italia in Pretoria, 796, George Avenue,0083 Arcadia, Pretoria, South AfricaandIstituto Nazionale di Astrofisica, Istituto di Radioastronomia, Area della Ricerca, Via Gobetti 101, I-40127, Bologna,ItalyEmail: pretoria.scienza@esteri.itviii

Introduction to the Proceedings of WGTTG2021

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Introduction to the Proceedings of WGTTG2021

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