21 citations · 31 across the 14 of their papers we have counts for
19 papers
New Results on Difference Distance Magic Labelings
Roza Aceska, Niny Arcila-Maya, Joshua Carlson +5
A graph labeling assigns values to the components of a graph (vertices, edges, etc.). In particular, distance magic labelings have been widely studied in undirected graphs. In such…
Isomorphisms and properties of TAR reconfiguration graphs for zero forcing and other -set parameters
Novi H. Bong, Joshua Carlson, Bryan Curtis +2
An -TAR (token addition/removal) reconfiguration graph has as its vertices sets that satisfy some property , with an edge between two sets if one is obtained from the other b…
The multi-robber damage number of a graph
Joshua Carlson, Meghan Halloran, Carolyn Reinhart
In many variants of the game of Cops and Robbers on graphs, multiple cops play against a single robber. In 2019, Cox and Sanaei introduced a variant of the game that gives the robb…
Minimal Zero Forcing Sets
Boris Brimkov, Joshua Carlson
In this paper, we study minimal (with respect to inclusion) zero forcing sets. We first investigate when a graph can have polynomially or exponentially many distinct minimal zero f…
Generalizing forbidden induced subgraph characterizations of high throttling numbers
Jurgen Kritschgau, Josh Carlson
Zero forcing is a process that models the spread of information throughout a graph as white vertices are forced to turn blue using a color change rule. The idea of throttling, intr…
The Hopping Forcing Rule
Joshua Carlson, John Petrucci
Zero forcing is a combinatorial game played on graphs that can be used to model the spread of information with repeated applications of a color change rule. In general, a zero forc…
Throttling for standard zero forcing on directed graphs
Emily Cairncross, Joshua Carlson, Peter Hollander +3
Zero forcing is a process on graphs in which a color change rule is used to force vertices to become blue. The amount of time taken for all vertices in the graph to become blue is…
The damage throttling number of a graph
Joshua Carlson, Robin Eagleton, Jesse Geneson +3
The cop throttling number of a graph, introduced in 2018 by Breen et al., optimizes the balance between the number of cops used and the number of rounds required to catch the robbe…
Parking Functions: Choose Your Own Adventure
Joshua Carlson, Alex Christensen, Pamela E. Harris +2
Warning. The reading of this paper will send you down many winding roads toward new and exciting research topics enumerating generalized parking functions. Buckle up!
Sequences of consecutive factoradic happy numbers
Joshua Carlson, Eva G. Goedhart, Pamela E. Harris
Given a positive integer , the factorial base representation of is given by , where and for all . For…
Various Characterizations of Throttling Numbers
Joshua Carlson, Juergen Kritschgau
Zero forcing can be described as a combinatorial game on a graph that uses a color change rule in which vertices change white vertices to blue. The throttling number of a graph min…
Antimagic orientations of graphs with large maximum degree
Donglei Yang, Joshua Carlson, Andrew Owens +5
Given a digraph with arcs, a bijection is an antimagic labeling of if no two vertices in have the same vertex-sum, where t…
Optimizing the trade-off between number of cops and capture time in Cops and Robbers
Anthony Bonato, Jane Breen, Boris Brimkov +6
The cop throttling number of a graph for the game of Cops and Robbers is the minimum of , where is the number of cops and is the minimu…
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…
Throttling positive semidefinite zero forcing propagation time on graphs
Joshua Carlson, Leslie Hogben, Jürgen Kritschgau +4
Zero forcing is a process on a graph that colors vertices blue by starting with some of the vertices blue and applying a color change rule. Throttling minimizes the sum of the size…
Throttling for Zero Forcing and Variants
Joshua Carlson
Zero forcing is a process on a graph in which the goal is to force all vertices to become blue by applying a color change rule. Throttling minimizes the sum of the number of vertic…
Lower Bounds for the Exponential Domination Number of
Chassidy Bozeman, Joshua Carlson, Michael Dairyko +2
A vertex in a porous exponential dominating set assigns weight to vertex . A porous exponential dominating set of a graph is a su…
Throttling for the game of Cops and Robbers on graphs
Jane Breen, Boris Brimkov, Joshua Carlson +3
We consider the cop-throttling number of a graph for the game of Cops and Robbers, which is defined to be the minimum of , where is the number of co…
Ordered multiplicity inverse eigenvalue problem for graphs on six vertices
John Ahn, Christine Alar, Beth Bjorkman +6
For a graph , we associate a family of real symmetric matrices, , where for any , the location of the nonzero off-diagonal entries of a…