Computer assisted discovery: Zero forcing vs vertex cover

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In this paper, we showcase the process of using an automated conjecturing program called \emph{TxGraffiti} written and maintained by the second author.

• We begin by proving a conjecture formulated by \emph{TxGraffiti} that for a claw-free graph $G$, the vertex cover number $\beta(G)$ is greater than or equal to the zero forcing number $Z(G)$.
• Our proof of this result is constructive, and yields a polynomial time algorithm to find a zero forcing set with cardinality $\beta(G)$.
• We also use the output of \emph{TxGraffiti} to construct several infinite families of claw-free graphs for which $Z(G)=\beta(G)$.