Research Trends in Graph Theory and Applications

1. Front Matter

   Pages i-xviii

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2. Finding Long Cycles in Balanced Tripartite Graphs: A First Step

   • Gabriela Araujo-Pardo, Zhanar Berikkyzy, Jill Faudree, Kirsten Hogenson, Rachel Kirsch, Linda Lesniak et al.

   Pages 1-10

3. Product Thottling

   • Sarah E. Anderson, Karen L. Collins, Daniela Ferrero, Leslie Hogben, Carolyn Mayer, Ann N. Trenk et al.

   Pages 11-50

4. Analysis of Termatiko Sets in Measurement Matrices

   • Katherine F. Benson, Jessalyn Bolkema, Kathryn Haymaker, Christine Kelley, Sandra R. Kingan, Gretchen L. Matthews et al.

   Pages 51-71

5. The Threshold Dimension and Threshold Strong Dimension of a Graph: A Survey

   • Nadia Benakli, Novi H. Bong, Shonda Dueck (Gosselin), Beth Novick, Ortrud R. Oellermann

   Pages 73-98

6. Symmetry Parameters for Mycielskian Graphs

   • Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, K. E. Perry, Puck Rombach

   Pages 99-117

7. Reconfiguration Graphs for Dominating Sets

   • Kira Adaricheva, Chassidy Bozeman, Nancy E. Clarke, Ruth Haas, Margaret-Ellen Messinger, Karen Seyffarth et al.

   Pages 119-135

The Workshop for Women in Graph Theory and Applications was held at the Institute for Mathematics and Its Applications (University of Minnesota, Minneapolis) on August 19-23, 2019. During this five-day workshop, 42 participants performed collaborative research, in six teams, each focused on open problems in different areas of graph theory and its applications. The research work of each team was led by two experts in the corresponding area, who prior to the workshop, carefully selected relevant and meaningful open problems that would yield high-quality research and results of strong impact. As a result, all six teams have made significant contributions to several open problems in their respective areas. The workshop led to the creation of the Women in Graph Theory and Applications Research Collaboration Network, which provided the framework to continue collaborating and to produce this volume.


This book contains six chapters, each of them on one of the different areas of research at the Workshop for Women in Graph Theory and Applications, and written by participants of each team.

• graph symmetries
• metric dimension
• graph searching
• data storage
• power domination
• throttling

• Department of Mathematics, Texas State University, San Marcos, USA

  Daniela Ferrero

• Department of Mathematics, Iowa State University, Ames, USA

  Leslie Hogben

• Department of Mathematics, Brooklyn College and the Graduate Center, City University of New York, New York, USA

  Sandra R. Kingan

• Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA

  Gretchen L. Matthews

​Daniela Ferrero is a Professor of Mathematics at Texas State University-San Marcos, TX. Her expertise is on graph theory and her research focuses on combinatorial optimization problems arising in science, engineering, and in other fields of mathematics. Her research program has been funded by the National Science Foundation, the National Security Agency, the American Mathematical Society, the Mathematical Association of America and AWM. Her initiatives to promote inclusion in mathematics through collaborative research include mentoring programs for graduate and undergraduate students at her home institution and the co-organization of the Workshop for Women in Graph Theory and Applications, which led to the creation of the AWM Research Collaboration Network for Women in Graph Theory and Applications. She earned a degree on Computer Engineering from Universidad de la República (Montevideo, Uruguay) and a Ph.D. in Applied Mathematics and Telematics from Universitat Politècnica deCatalunya (Barcelona, Spain). Prior to joining Texas State University, she was a postdoctoral research fellow at the Institute of Information Science of Academia Sinica (Taipei, Taiwan).
Leslie Hogben is a Professor of Mathematics and Associate Dean for Graduate Studies and Faculty Development at Iowa State University, and the Associate Director for Diversity at the American Institute of Mathematics. She received her B.A. from Swarthmore College in 1974, and her Ph.D. in 1978 from Yale University under the direction of Nathan Jacobson. Although originally working in nonassociative algebras, in the mid-1990s she changed her focus to linear algebra, especially combinatorial matrix theory and spectral graph theory, and in the past ten years has become more involved in graph theory. Dr. Hogben is the author of more than 100 research papers and is a Fellow of the American Association for the Advancement of Science and of the Association for Women in Mathematics. She is the editor of Handbook of Linear Algebra, an advisory editor of Electronic Journal of Linear Algebra, and an associate editor of Linear Algebra and its Applications and is a frequent co-organizer of meetings, workshops, and special sessions/mini-symposia, including the 2017 International Linear Algebra Society Conference. She particularly enjoys introducing students to mathematical research. She has advised or is advising 5 postdoctoral associates, 22 doctoral students, 19 masters students, and 40 undergraduate researchers and is the PI of the NSF-sponsored Research Training Group in combinatorics at ISU and was formerly the PI of the ISU Math REU.


Sandra R. Kingan is an Associate Professor at Brooklyn College and the Graduate Center of the City University of New York. Her research lies at the intersection of combinatorics and geometry. She has published papers in matroid theory, graph theory, and combinatorial algorithms and her work is supported by theNational Science Foundation. Her book "Graphs and Networks" blends classical graph theory with modern network science and is available for preorder. She earned a BS from St. Xavier's College, Mumbai, India and a PhD from Louisiana State University. She is a co-organizer of the Women in Graph Theory Research Network, a Math Alliance mentor and an International Mathematical Union's Committee for Women ambassador for North America.


Gretchen L. Matthews is a Professor of Mathematics at Virginia Tech and Director of the Commonwealth Cyber Initiative Southwest Virginia. She is affiliated faculty with Virginia Tech’s Hume Center for National Security & Technology and Computational Modeling & Data Analytics program. Her research is in applied algebra, with a focus on coding theory and cryptography and applications in data storage, protection, and privacy. She is an AWM Fellow, in recognition of her efforts to broaden participation in mathematics. She earned a BS fromOklahoma State University and a PhD from Louisiana State University, both in Mathematics. She spent time as a postdoc at University of Tennessee and on the faculty at Clemson University before joining Virginia Tech.

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