Discrete & Computational Math Seminar: Darren Narayan
Discrete & Computational Math Seminar (DisCoMath)
Failed Zero Forcing Numbers of Graphs
Darren Narayan
School of Mathematical Sciences
Rochester Institute of Technology
Abstract: Given a graph πΊ, the zero forcing number of πΊ, π(πΊ), is the smallest cardinality of any set π of vertices on which repeated applications of the forcing rule results in all vertices being in π. The forcing rule is: if a vertex π£ is in π, and exactly one neighbor π’ of π£ is not in π, then π’ is added to π in the next iteration. Zero forcing numbers have attracted great interest over the past 15 years and have been well studied. In this paper, we investigate the largest size of a set π that does not force all of the vertices in a graph to be in π. This quantity is known as the failed zero forcing number of a graph and will be denoted by πΉ(πΊ). We present new results involving this parameter.
Intended Audience: Undergraduates
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