Research

Research Topics

• commutative algebra

• homological algebra

• combinatorial commutative algebra

• algebraic number theory

• graph theory

• poset theory

• network science

Research

• CV

Referred Research Papers

1. Homology of Artinian and Matlis Reflexive Modules I, with M. J. Leamer and S. Sather-Wagstaff, J. Pure Appl. Algebra 215 (2011), no. 10, 2486-2503. arXiv version

2. Homology of Artinian and Matlis Reflexive Modules II, with M. J. Leamer and S. Sather-Wagstaff, J. of Algebra 403 (2014), 229-272. arXiv version

3. Quasidualizing Modules, J. of Comut. Algebra 2 (2014), no. 2, 209-229. arXiv version

4. Path Ideals of Weighted Graphs, with S. Sather-Wagstaff, J. Pure Appl. Algebra, 219 (2015), 3889-3912. arXiv version

5. Lattice Point Visibility on Generalized Lines of Sight, with E.H.Goins, P.Harris, and a.Mbirika, Amer. Math. Monthly 125 Issue 7 (2018), arXiv version.

6. The Graph of Critical Pairs of a Crown, with F. Barrera-Cruz, R. Garcia, P. Harris, H. Smith, S. Talbott, L. Taylor, and W. Trotter, Order, 1-32 (2019), https://doi.org/10.1007/s11083-019-09485-4, arXiv version.

7. Block Circulant Graphs and the Graphs of Critical Pairs of Crowns, with R. Garcia, P. Harris, and S. Talbott, AKCE, (2019).

8. Characterizing Graphs of Critical Pairs of Layered Generalized Crowns, with R. Garcia, P. Harris, and S. Talbott, Electronic Journal of Graph Theory and Applications, 7 (2) (2019).

9. τ-Atomicity and Quotients of Size Four, with R. Hasenauer, Tamkang Journal of Mathematics, 52 (2021), https://doi.org/10.5556/j.tkjm.52.2021.3241.

10. Upper Broadcast Domination of Toroidal Grids and a Classification of Diametrical Trees, with E. Insko and C. Price, arXiv version, submitted.

11. Decomposition of complete graphs into tri-cyclic graphs with eight edges, with D. Froncek, J. of Comb. Math. and Comb. Computing, 114 (2020).

12. Atomic Density of Numerical Semigroup Algebras, with A.Antoniou, R.A.C.Edmonds, C.O'Neill, and S.Talbott, arXiv version, J. of Commut. Algebra, accepted.