# Graduate Seminar Series

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Wed., Apr. 5, 2023 3:30 p.m.
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Location: CK 185 and Live Stream
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**Speaker**: Brenda Andrusiak

**Title:** On graphs with equal Zero Forcing and Path Covering Numbers (76 kB)

**Abstract:**

Building from my first presentation, we present some recent work on a class of graphs denoted by ZP. A graph G is in ZP if the zero forcing and path covering number of H are equal for every induced subgraph H of G. We pay particular attention to planar and outerplanar graphs and provide a complete characterization for the case when the path cover number of G is two. This result relies on a careful analysis of so-called 'terminal' vertices with respect to both the zero forcing process and optimal path coverings. We conclude with a new result showing that the class ZP is closed under the graph operation of vertex sums, which can be used to re-prove a known result stating that cactii graphs belong to ZP.

**Live Stream:**