Forcing Parameters in Fully Connected Cubic Networks

Abstract

Domination in graphs has been extensively studied and adopted in many real life applications. The monitoring electrical power system is a variant of a domination problem called power domination problem. Another variant is the zero forcing problem. Determining minimum cardinality of a power dominating set and zero forcing set in a graph are the power domination problem and zero forcing problem, respectively. Both problems are NP-complete. In this paper, we compute the power domination number and the zero forcing number for fully connected cubic networks.