Joshua Carlson

activity

20172026

most citedThrottling positive semidefinite zero forcing propagation time on graphs

21 citations · 31 across the 14 of their papers we have counts for

collaborators

Showing 2019Show all

4 papers · 1 filter

math.NT2019

Sequences of consecutive factoradic happy numbers

Joshua Carlson, Eva G. Goedhart, Pamela E. Harris

Given a positive integer $n$ , the factorial base representation of $n$ is given by $n = \sum_{i = 1}^{k} a_{i} \cdot i!$ , where $a_{k} \neq = 0$ and $0 \leq a_{i} \leq i$ for all $1 \leq i \leq k$ . For…

math.CO2019

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…

math.CO2019★ 3 cited

Antimagic orientations of graphs with large maximum degree

Donglei Yang, Joshua Carlson, Andrew Owens +5

Given a digraph $D$ with $m$ arcs, a bijection $τ : A (D) \to {1, 2, \dots, m}$ is an antimagic labeling of $D$ if no two vertices in $D$ have the same vertex-sum, where t…

math.CO2019

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 $t h_{c} (G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + c a p t_{k} (G)$ , where $k$ is the number of cops and $c a p t_{k} (G)$ is the minimu…