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Found 4 Results
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Breaking Symmetries of Mycielskian Graphs and of Cubes

The distinguishing number of a graph is the least number of colors in a vertex coloring such that the only color-preserving automorphism is trivial. The determining number of a graph is size of a smallest set of vertices $S$ such that the only automorphism fixing $S$ (point-wise) is trivial. I will discuss results on these symmetry parameters for Mycielskian [Read More...]

Presenter: Sarah Loeb, Hampden-Sydney College
Authors: Debra Boutin, Sally Cockburn, Lauren Keough, Sarah Loeb, Kat Perry, Puck Rombach
Symposium Year: 2022
Session: Women in Graph Theory and Applications
Presentation Time: June 17, 2022; 10:15 am

On a relation between bipartite biregular cages, block designs and generalized polygons*

A $\textit{bipartite biregular}$ $(m,n;g)$-graph $\Gamma$ is a bipartite graph of even girth $g$ having the degree set $\{m,n\}$ and satisfying the additional property that the vertices in the same partite set have the same degree. An $(m,n;g)$-$\textit{bipartite biregular cage}$ is a bipartite biregular $(m,n;g)$-graph of minimum order. In this [Read More...]

Presenter: Gabriela Araujo-Pardo, Universidad Nacional Autónoma de México
Authors: Gabriela Araujo-Pardo, Robert Jajcay, Alejandra Ramos-Rivera and Tamás Szönyi
Symposium Year: 2022
Session: Women in Graph Theory and Applications
Presentation Time: June 17, 2022; 10:40 am

Product Throttling for Power Domination

Power domination is a particular form of graph searching in which an initial step of standard graph domination is followed by a zero forcing process. Power domination was introduced independently from zero forcing, as a model for the monitoring process of electrical power networks. As electrical power systems become increasingly more complex, so does their [Read More...]

Presenter: Daniela Ferrero, Texas State University
Authors: Sarah E. Anderson; Karen L. Collins; Daniela Ferrero; Leslie Hogben; Carolyn Mayer; Ann N. Trenk; Shanise Walker
Symposium Year: 2022
Session: Women in Graph Theory and Applications
Presentation Time: June 17, 2022; 11:05 am

Graph-based codes based on dyadic matrices

Reproducible parity check codes have parity check matrices that can be specified by a few rows along with a set of transformations on those rows. Some examples of reproducible codes include array-based LDPC codes with dyadic or $n$-adic matrices as blocks. When such a block has weight $j$, it can be viewed as a sum of $j$ permutation matrices. In this talk [Read More...]

Presenter: Christine Kelley, University of Nebraska-Lincoln
Authors: Christine Kelley and Meraiah Martinez
Symposium Year: 2022
Session: Women in Graph Theory and Applications
Presentation Time: June 17, 2022; 11:30 am
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