Associate Professor, University of Winnipeg Office: 6L05 Lockhart Hall Phone: (204) 786-9346 E-mail: sm.dueck@uwinnipeg.ca

Shonda Dueck (Gosselin) Dept. of Mathematics and Statistics University of Winnipeg 515 Portage Avenue Winnipeg, Manitoba CANADA R3B 2E9

Teaching

Fall Term 2022: MATH-1401 Discrete Math MATH-1201 Linear Algebra I MATH-3401 Graph Theory

Winter Term 2022: MATH-1201 Linear Algebra I MATH-2106 Intermediate Calculus II

Research Interests

My research is in the area of algebraic graph theory. I am interested in the action of groups on graphs and hypergraphs. Recently I have studied cyclic partitions of complete hypergraphs, which can be viewed as generalized self-complementary graphs. Currently I am working on using algebraic techniques to construct hypergraph decompositions on different groups. I am also interested in the problem of determining the metric dimension of Cayley hypergraphs and circulant graphs.

Publications

Nadia Benakli, Novi H. Bong, Shonda M. Dueck, Linda Eroh, Beth Novick, Ortrud R. Oellermann. The Threshold Strong Dimension of a Graph. Discrete Mathematics, Volume 344, Issue 7, July 2021, 112402. https://doi.org/10.1016/j.disc.2021.112402

http://arxiv.org/abs/2008.04282\\

Dilbarjot, Shonda Dueck, Cyclic decompositions of complete and almost complete uniform hypergraphs. Discussiones Mathematicae Graph Theory, Volume 42 (2022), 747-759.

https://doi.org/10.7151/dmgt.2303.

S.Gosselin, Almost t-complementary uniform hypergraphs. Aequationes Mathematicae (2019), http://link.springer.com/article/10.1007/s00010-018-0631-y

K. Chau and S. Gosselin, The metric dimension of circulant graphs and their Cartesian products. Opuscula Mathematica, Volume 37, no. 4 (2017), pp. 509-534.

A. Borchert and S. Gosselin, The metric dimension of circulant graphs and Cayley hypergraphs. Utilitas Mathematica, Volume 106, (2018), 125 - 147.

S. Gosselin, A. Szymański and A.P. Wojda, Cyclic partitions of complete nonuniform hypergraphs and complete multipartite hypergraphs. Discrete Mathematics & Theoretical Computer Science, Volume 15, no. 2 (2013), pp. 215-222.

G. Andruchuk and S. Gosselin, A note on Hamiltonian circulant digraphs of outdegree three. Open Journal of Discrete Mathematics, Volume 2 (2012), pp. 160-163.

G. Andruchuk, S. Gosselin and Y. Zheng, Hamiltonian Cayley digraphs on direct products of dihedral groups. Open Journal of Discrete Mathematics, Volume 2 (2012), pp. 88-92.

S. Gosselin. Self-complementary non-uniform hypergraphs. Graphs and Combinatorics, Volume 28 (2012), pp. 615-635.

S. Gosselin. Constructing regular self-complementary uniform hypergraphs. Journal of Combinatorial Designs, Volume 19 (2011), pp. 439-454.

S. Gosselin. Vertex-transitive q-complementary uniform hypergraphs. Electronic Journal of Combinatorics, Volume 18 (2011), no. 1, Research Paper 100, 19 pp.

S. Gosselin. Cyclically t-complementary uniform hypergraphs. European Journal of Combinatorics, Volume 31 (2010), pp. 1629-1636.

S. Gosselin. Generating self-complementary uniform hypergraphs. Discrete Mathematics, Volume 310 (2010), pp. 1366-1372.

S. Gosselin. Vertex-transitive self-complementary uniform hypergraphs of prime order. Discrete Mathematics, Volume 310 (2010), pp. 671-680.

M. Fehr, S. Gosselin and O. Oellermann. The partition dimension of Cayley digraphs. Aequationes Mathematicae, Volume 71 (2006), pp. 1-18.

M. Fehr, S. Gosselin and O. Oellermann. The metric dimension of Cayley digraphs. Discrete Mathematics, Volume 306 (2006), pp. 31-41.

Book Chapters

Nadia Benakli, Novi H. Bong, Shonda M. Dueck, Beth Novick, Ortrud R. Oellermann. Chapter 4 - The Threshold Dimension and Threshold Strong Dimension of a Graph: a Survey. WIGA 2019 AWM volume, Research Trends in Graph Theory and Applications, Copyright 2021, Springer.

Dissertations

S. Gosselin. Self-complementary hypergraphs. Ph.D. Thesis, University of Ottawa (2009).

S. Gosselin. Regular two-graphs and equiangular lines. Masters Thesis, University of Waterloo (2004).

My CV

Last update: September 12, 2022.