DiscoMath Seminar: The Zero Forcing Span of a Graph
Discrete & Computational Math Seminar (DisCoMath)
Bringing Together Zero Forcing and Failed Zero Forcing: The Zero Forcing Span of a Graph
Dr. Bonnie Jacob
Associate Professor
School of Mathematical Sciences, RIT
Abstract:
Between the zero forcing number of a graph Z(G) and the failed zero forcing number F(G) is where anything can happen. More specifically, if Z(G)≤k<F(G), there exist sets of cardinality k that are zero forcing sets, and sets of cardinality k that are not. For some graphs, there are many such cardinalities (or equivalently, the difference between Z(G) and F(G) is large), while for others, there are none. We call the number of such cardinalities the zero forcing span of a graph. In this talk, we connect results on Z(G) with results on F(G) to describe graphs that have various zero forcing spans, providing characterizations of some extreme values.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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