31 citations
- Arizona State UniversityUS3 papers
- Metropolitan State UniversityUS2 papers
- Brigham Young UniversityUS1 paper
- Claremont McKenna CollegeUS1 paper
- Commonwealth Scientific and Industrial Research OrganisationAU1 paper
- Concordia UniversityCA1 paper
- Data61AU1 paper
- Fraunhofer Institute for Communication, Information Processing and ErgonomicsDE1 paper
- Fraunhofer Institute for Material Flow and LogisticsDE1 paper
- Houghton UniversityUS1 paper
- Juniata CollegeUS1 paper
- Karlsruhe Institute of TechnologyDE1 paper
5 papers · 1 filter
Orthogonal representations of Steiner triple system incidence graphs
Louis Deaett, H. Tracy Hall
The Heawood graph is the point-block incidence graph of the Fano plane (the unique Steiner triple system of order 7). We show that the minimum semidefinite rank of this graph is 10…
The minimum rank problem for circulants
Louis Deaett, Seth A. Meyer
The minimum rank problem is to determine for a graph the smallest rank of a Hermitian (or real symmetric) matrix whose off-diagonal zero-nonzero pattern is that of the adjacenc…
Optimal Pebbling in Products of Graphs
David S. Herscovici, Benjamin D. Hester, Glenn H. Hurlbert
We prove a generalization of Graham's Conjecture for optimal pebbling with arbitrary sets of target distributions. We provide bounds on optimal pebbling numbers of products of comp…
Generalizations of Graham's Pebbling Conjecture
David S. Herscovici, Benjamin D. Hester, Glenn H. Hurlbert
We investigate generalizations of pebbling numbers and of Graham's pebbling conjecture that pi(GxH) <= pi(G)pi(H), where pi(G) is the pebbling number of the graph G. We develop new…
t-Pebbling and Extensions
David S. Herscovici, Benjamin D. Hester, Glenn H. Hurlbert
Graph pebbling is the study of moving discrete pebbles from certain initial distributions on the vertices of a graph to various target distributions via pebbling moves. A pebbling…