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Rhodes>Mathematics>People>Staff>Eric Andriantiana

Prof. Eric Andriantiana

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Associate Professor (and Head of Department)

MSC (Stellenbosch), PhD (Stellenbosch)

e.andriantiana@ru.ac.za

Room 2 Maths Building (Drostdy Lodge)

(046) 603 7444

Teaching

  • Introduction to Algebra (In MAM2): Set theory; mappings; binary operations; equivalence relations and order; groups.
  • Introduction to Analysis (In MAM2): Real numbers; open and closed intervals; sequences and series (convergence); functions of a real variable (continuity, limit); series of functions; Taylor series.
  • Discrete Mathematics (in MAT 315): Arithmetic, Combinatorics, Graph Theory.
  • Algebraic Graph Theory: An honours course on graphs, their adjacency matrices, Laplacian matrices, characteristic polynomials and spectrum.
  • Honours Projects: Topics on Algebra, graph theory, combinatorics and their applications are available. Contact me for more details.
  • Experimental Mathematics (2016,2017,2019) at the African Institute for Mathematical Sciences (AIMS): The course ilustrates how mathematical ideas evolve from experimental observations to theorems. It involves Number Theory, Linear Algebra, Probability, Graph Theory, and it uses SAGE.

Students 

  • 2013: The Energy of a Graph, Valisoa Razanajatovo Misanantenaina, AIMS MSc, (co-supervisor S. Wagner).
  • 2015: Matrices of Graphs, Sindisiwe McDonald, RU Honours project.
  • 2017: Tadpoles With Large Spectral Moment, Boqwana Mhlanguleli, RU Honours project. 
  • 2018: Strictly Bicyclic Graph With Minimum Wienner Index, Xhanti Sinoxolo, RU Honours project.
  • 2018-2019: Grabcuts for Image Sementation: A comparative Study of Clustering Techiniques, by Nozuko Zuleika Manzi, UFH MSc, (co-supervisor Prof B. Makamba)
  • 2019: Number of walks in 2-segment and 3-segment graphs, Brian Welman,  RU Honours project.
  • 2019-2020: On the Wiener index of bicyclic graphs and graphs with given segnt sequence, Xhanti Sinoxolo, RU MSc.
  • 2022: The Binary Balanced Caterpillar and Condensed Greedy Tree: Extremal in number of subtrees amongst trees with required number of branching points, Asher Pearse, RU Honours project.
  • 2022: Matchings in Subcubic Graphs, William Kalukango,  AIMS MSc,  (co-supervised by Dr Zekhaya Shozi).
  • 2023: Number of subtrees of caterpillars with given degree sequence, Liteboho Samuel Sekholomi, AIMS MSc.
  • 2024: The number of independent subsets and the energy of caterpillars under degree restriction, Xhanti Sinoxolo, RU PhD.

Research interests

  • Graph Theory
  • Combinatorics

Selected publications

  • Nordhaus-Gaddum inequalities for the number of connected induced subgraphs in graphs, Quaestiones Mathematicae 45 (8) (2022), 1191-1213, with AAV Dossou-Olory, Full text, Preprint.
  • Trees with minimum number of infima closed sets, Discrete Mathematics 345 (5) (2022), 112793, with S Wagner, Full text, Preprint
  • Extremal Trees with Fixed Degree Sequence, The electronic journal of combinatorics 28 (1) (2021), P1.1, V Razanajatovo Misanantenaina, S Wagner, Free full text.
  • The average size of independent sets of graphs, European Journal of Mathematics 6 (2) (2020), 561-576, with  V Razanajatovo Misanantenaina, S Wagner, Full text, Preprint.
  • The Average Size of Matchings in Graphs, Graphs and Combinatorics  36 (2020) 539-560, With V Razanajatovo Misanantenaina, S Wagner, Preprint
  • Subtrees and Independent Subsets in Unicyclic Graphs and Unicyclic Graphswith Fixed Segment Sequence, MATCH Commun. Math. Comput. Chem. 84 (2020) 537-566, With H. Wang, Full text.
  • The average size of independent sets of graphs, European Journal of Mathematics (2020) 6:561-576,  With V Razanajatovo Misanantenaina, S Wagner, Free full text.
  • The ancestral matrix of a rooted tree, Linear Algebra and its Applications 575 (2019) 35–65, With Kenneth Dadedzi, Stephan Wagner, Free full text.
  • Extremal problems for trees with given segment sequence, Discrete Applied Mathematics 220 (2017) 20–34. With S. Wagner and H. Wang. Full text.
  • Maximum Wiener index of trees with given segment sequence, MATCH Communications in Mathematical and in Computer Chemistry, 75 (2016) 91-104. With S. Wagner and H. Wang. Full text.
  • Graphs with maximal Hosoya index and minimal Merrifield-Simmons index, Discrete Mathematics, 329 (2014) 77-87. With Z. Zhu, C. Yuan and S. Wagner.   Full text. 
  • Spectral moment of trees with given degree sequence, Linear Algebra Appl. 439 (2013) 3980-4002. With S. Wagner. Preprint.
  • Greedy trees, subtrees and antichains, Electron. J. Combin. 20(3) (2013), 28. With S. Wagner and H. Wang,  Free full text.
  • Energy, Hosoya index and Merrifield-Simmons index of trees with prescribed degree sequence, Discrete Appl. Math. 161 (2013) 724-741. Full text.
  • More Trees with Large Energy and Small Size, MATCH Commun. Math. Comput. Chem., 68 (2012) 697-702; with I. Gutman, B. Furtula and M. Cvetic. Free full text.
  • More Trees with Large Energy, MATCH Commun. Math. Comput. Chem., 68 (2012) 675-695. Free full text.
  • Unicyclic graphs with large energy, Linear Algebra and its Applications, 435 (2011) 1399-1414; with S. Wagner. Full text. 

Book chapters

  • Laplacian Energy, in Energies of Graphs -Theory and Applications , Gutman, X. Li (Eds.) , Univ. Kragujevac, Kragujevac, 2016, pp. 49-80.
  • Bounds of the Estrada Index and the Laplacian Estrada Index, in Bounds in Chemical Graph Theory - Mainstreams, I. Gutman, B. Furtula, K. C. Das, E. Milovanovic, I. Milovanovic (Eds.),Univ. Kragujevac, Kragujevac, 2017, pp. 23-52.

Awards and ratings

  • 2021: C   NRF rating
  • 2017: (RU) Claude Leon Merit Award
  • 2015: Y   NRF Rating

Others (professional involvement, community engagements ...)

  • (Rhodes') Regional Coordinanator for the Siyanqoba Olympiad training.
  • (Rhodes') Regional Coordinanator for the South African Tertiary Mathematics Olympiad (SATMO).
  • I served as a reviewer for Mathematical Reviews and journals including Discrete Applied Mathematics, Applied Mathematics Letters, Computers & Mathematics with Applications, MATCH Communications in Mathematical and in Computer Chemistry, Applied Mathematics-A Journal of Chinese Universities, Quaestiones Mathematicae, Theory and Applications of Graphs, Linear Algebra and its Applications, Applicable Analysis and Discrete Mathematics, Transactions on Network Science and Engineering.

Last Modified: Sat, 13 Apr 2024 07:05:33 SAST