1 citations · 2 across the 15 of their papers we have counts for
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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…
Reconfiguration of Minimum PSD Forcing Sets and Minimum Skew Forcing Sets
Novi Bong, Mary Flagg, Mark Hunnell +4
Reconfiguration graphs provide a way to represent relationships among solutions to a problem, and have been studied in many contexts. We investigate the reconfiguration graphs corr…
A Characterization of Claw-Free Graphs using Zero Forcing Invariants
Randy Davila, Houston Schuerger, Ben Small
We prove that the \emph{standard zero forcing number} and the \emph{positive semidefinite zero forcing number} are equal for all claw-free graphs . This result r…
Zero Forcing and Vertex Independence Number on Cubic and Subcubic Graphs
Houston Schuerger, Nathan Warnberg, Michael Young
Motivated by a conjecture from the automated conjecturing program TxGraffiti, in this paper the relationship between the zero forcing number, , and the vertex independence nu…
The Zero Forcing Numbers of Peony Graphs and Web Graphs
Sara Anderton, Kanno Mizozoe, Houston Schuerger +1
The concept of zero forcing involves a dynamic coloring process by which blue vertices cause white vertices to become blue, with the goal of forcing the entire graph blue while cho…
Landscapes of the Octahedron
Emiko Saso, Houston Schuerger, Xin Shi
The landscapes of a polyhedron are subsets of its nets one must consider to identify all shortest paths. Landscapes of cubes and tetrahedra have been used to identify coordinate ba…
The zero forcing numbers and propagation times of gear graphs and helm graphs
Sara Anderton, Rilee Burden, McKenzie Fontenot +8
Zero forcing is a dynamic coloring process on graphs. Initially, each vertex of a graph is assigned a color of either blue or white, and then a process begins by which blue vertice…
Forts, (fractional) zero forcing, and Cartesian products of graphs
Thomas R. Cameron, Leslie Hogben, Franklin H. J. Kenter +2
The (disjoint) fort number and fractional zero forcing number are introduced and related to existing parameters including the (standard) zero forcing number. The fort hypergraph is…
New Structures and their Applications to Variants of Zero Forcing and Propagation Time
Leslie Hogben, Mark Hunnell, Kevin Liu +3
We introduce a generalization of the concept of a chronological list of forces, called a relaxed chronology. This concept is used to introduce a new way of formulating the standard…
The Strong Spectral Property of Graphs: Graph Operations and Barbell Partitions
Sarah Allred, Emelie Curl, Shaun Fallat +4
The utility of a matrix satisfying the Strong Spectral Property has been well established particularly in connection with the inverse eigenvalue problem for graphs. More recently t…
Computer assisted discovery: Zero forcing vs vertex cover
Boris Brimkov, Randy Davila, Houston Schuerger +1
In this paper, we showcase the process of using an automated conjecturing program called \emph{TxGraffiti} written and maintained by the second author. We begin by proving a conjec…
Graphs which satisfy a Vizing-like bound for power domination of Cartesian products
Sarah E. Anderson, Kirsti Kuenzel, Houston Schuerger
Power domination is a two-step observation process that is used to monitor power networks and can be viewed as a combination of domination and zero forcing. Given a graph , a su…
Upper Bounds for Positive Semidefinite Propagation Time
Leslie Hogben, Mark Hunnell, Kevin Liu +3
The tight upper bound is established for the pos…