2 citations · 2 across the 2 of their papers we have counts for
6 papers
Connected power domination in graphs
Boris Brimkov, Derek Mikesell, Logan Smith
The study of power domination in graphs arises from the problem of placing a minimum number of measurement devices in an electrical network while monitoring the entire network. A p…
Restricted power domination and zero forcing problems
Chassidy Bozeman, Boris Brimkov, Craig Erickson +3
Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of…
Graphs with Extremal Connected Forcing Numbers
Boris Brimkov, Caleb C. Fast, Illya V. Hicks
Zero forcing is an iterative graph coloring process where at each discrete time step, a colored vertex with a single uncolored neighbor forces that neighbor to become colored. The…
Complexity and Computation of Connected Zero Forcing
Boris Brimkov
Zero forcing is an iterative graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. It is NP-hard to find a minimum ze…
Characterizations of the Connected Forcing Number of a Graph
Boris Brimkov, Randy Davila
Zero forcing is a dynamic graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. This forcing process has been used to…
A note on the clique number of complete -partite graphs
Boris Brimkov
In this note, we show that a complete -partite graph is the only graph with clique number among all degree-equivalent simple graphs. This result gives a lower bound on the c…