2 citations · 6 across the 7 of their papers we have counts for
6 papers · 1 filter
Graphs that are cospectral for the distance Laplacian
Boris Brimkov, Ken Duna, Leslie Hogben +4
The distance matrix of a graph is the matrix containing the pairwise distances between vertices, and the distance Laplacian matrix is $\mathcal{D}^L(G)=T(G)-\m…
On the status sequences of trees
Aida Abiad, Boris Brimkov, Alexander Grigoriev
The status of a vertex in a connected graph is the sum of the distances from to all other vertices. The status sequence of a connected graph is the list of the statuses of…
Power domination throttling
Boris Brimkov, Joshua Carlson, Illya V. Hicks +2
A power dominating set of a graph is a set that colors every vertex of according to the following rules: in the first timestep, every vertex in be…
Intersections, circuits, and colorability of line segments
Boris Brimkov, Jesse Geneson, Alathea Jensen +2
We derive sharp upper and lower bounds on the number of intersection points and closed regions that can occur in sets of line segments with certain structure, in terms of the numbe…
Optimal conditions for connectedness of discretized sets
Boris Brimkov, Valentin E. Brimkov
Constructing a discretization of a given set is a major problem in various theoretical and applied disciplines. An offset discretization of a set is obtained by taking the inte…
Power domination polynomials of graphs
Boris Brimkov, Rutvik Patel, Varun Suriyanarayana +1
A power dominating set of a graph is a set of vertices that observes every vertex in the graph by combining classical domination with an iterative propagation process arising from…