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 2024: On sabbatical

Winter Term 2025: MATH-1201 Linear Algebra I MATH-1401 Discrete Math MATH-3401 Graph Theory

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, and the threshold dimension and threshold strong dimension of a graph.

Publications

Tapendra BC and Shonda Dueck, On the metric dimension of circulant graphs, Opusculua Mathematics, 45, (2025), 9939-51.

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

Nadia Benakli, Novi H. Bong, Shonda M. Dueck, Linda Eroh, Ortrud R. Oellermann, The threshold strong dimension of a graph. Discrete Mathematics, Volume 344, Issue 7 (2021), 112402.

S.Gosselin, Almost t-complementary uniform hypergraphs. Aequationes Mathematicae (2019).

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 Book Chapters

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).

Last update: January 31, 2025.