I have completed several projects concerning domination in graphs, isolation in graphs, toughness of graphs, and well-hued graphs.
A full research statement is available upon request.
G. Boyer, W. Goddard, M. Henning. Bounds on the Total Isolation Number of (Regular) Bipartite Graphs. (Submitted 2025).
G. Boyer, W. Goddard, M. Henning. Domination, Isolation, and Matchings in (Cubic) Multigraphs and Inflations. (Submitted 2025)
G. Boyer, K. Kuenzel, J. Lyle, R. Pellico. Well-hued graphs with first difference two. (Submitted 2025). https://doi.org/10.48550/arXiv.2506.04993
G. Boyer, W. Goddard. On the toughness of regular graphs and prisms. (Submitted 2025). https://doi.org/10.48550/arXiv.2301.13632
G. Boyer, G. Farrell, W. Goddard. All-k-isolation in trees. (Submitted 2025)
G. Boyer, W. Goddard. Bounds on independent isolation in graphs. Disc. Appl. Math. 372 (2025), 143-149.
G.Boyer, W. Goddard, and M. Henning. On total isolation in graphs. Aequat. Math. (2024).
G. Boyer and W. Goddard, Disjoint isolating sets and graphs with maximum isolation number. Disc. Appl. Math. 356 (2024), 110-116.
G. Boyer, W. Goddard, and Michael Henning. Domination parameters and the removal of matchings. Appl. Math. and Comp. 476 (2023).
G.Boyer and W.Goddard. Domination in graphs and the removal of a matching. Discus. Math. Graph Theory 45 (1) (2023).