13 citations · 41 across the 24 of their papers we have counts for
32 papers
Throttling for metric dimension and its variants
Boris Brimkov, Peter Diao, Jesse Geneson +4
Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two availabl…
In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
Randy Davila, Boris Brimkov, Ryan Pepper
We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariant…
On the forts and related parameters of the hypercube graph
Boris Brimkov, Thomas R. Cameron, Owen Grubbs
In 2018, forts were defined as non-empty subsets of vertices in a graph where no vertex outside the set has exactly one neighbor in the set. Forts have since been used to character…
Graphs with degree sequence and
Boris Brimkov, Valentin Brimkov
In this paper we study the class of graphs that have the same degree sequence as two disjoint cliques and , as well as the class of the com…
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…
Extending a conjecture of Graham and Lovász on the distance characteristic polynomial
Aida Abiad, Boris Brimkov, Sakander Hayat +2
Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order is unimodal with the maximum val…