Skolem number of cycles and grid graphs - Carrigan, Braxton; Asplund, John (Theory and Applications of Graphs, 2021)
A Skolem sequence can be thought of as a labelled path where two vertices with the samelabelarethatdistanceapart.Thisconcepthasnaturallybeengeneralizedto labellingsofothergraphs,butalwaysusingatmosttwoofanyintegerlabel.Giventhat more than two vertices can be mutually distance d apart, wedefine a new generalization of aSkolemsequenceongraphsthatwecallaproperSkolemlabelling.Thisbrings rise tothequestion;use to proper Skolemlabel a graph?"This will be known as the Skolem number of the graph. In this paper we give the Skolem number for cycles and grid graphs,while also providing other related results along the way. Published by Digital Commons@Georgia Southern, 2021. © 2021 Georgia Southern University. All rights reserved.
0 citations (Crossref) [2023-10-31] Type: Article tex.citation: https://api.elsevier.com/content/abstract/scopus_id/85115356208
Keywords: dept.mat; peer-reviewed

Skolem Number of Subgraphs on the Triangular Lattice - Carrigan, Braxton; Green, Garrett (Communications on Number Theory and Combinatorial Theory, 2021)
Keywords: dept.mat; peer-reviewed

List colorings count rokudoku-pair squares - Carrigan, Braxton; Hammer, James; Lorch, John; Lorch, Robert; Owens, Caitlin (Bulletin of the Institute of Combinatorics and its Applications, 2021)
A rokudoku-pair square is an order-6 sudoku Latin square for both 2 x 3 and 3 x 2 tiling regions simultaneously. We count the distinct rokudoku-pair squares as well as orbits under the action of a suitable group. Our arguments employ group actions and list colorings of graphs. As an application we determine which rokudoku-pair squares are based on groups. © 2021. All Rights Reserved.
Type: Article tex.citation: https://api.elsevier.com/content/abstract/scopus_id/85109428650
Keywords: dept.mat; peer-reviewed; ⛔ No DOI found