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Kang, Eunjeong Yi","submitted_at":"2012-04-10T18:26:21Z","abstract_excerpt":"\\emph{Zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G) \\setminus S$ are colored white) such that $V(G)$ is turned black after finitely many applications of \"the color-change rule\": a white vertex is converted black if it is the only white neighbor of a black vertex. Zero forcing number was introduced and used to bound the minimum rank of graphs by the \"AIM Minimum Rank -- Special Graphs Work Group\". Let $G_1$ and $G_2$ be disjoint copies of a graph $G$ and let $f: V(G_1) \\rightarrow V(G_2)$ be a function. 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Kang, Eunjeong Yi","submitted_at":"2012-04-10T18:26:21Z","abstract_excerpt":"\\emph{Zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G) \\setminus S$ are colored white) such that $V(G)$ is turned black after finitely many applications of \"the color-change rule\": a white vertex is converted black if it is the only white neighbor of a black vertex. Zero forcing number was introduced and used to bound the minimum rank of graphs by the \"AIM Minimum Rank -- Special Graphs Work Group\". Let $G_1$ and $G_2$ be disjoint copies of a graph $G$ and let $f: V(G_1) \\rightarrow V(G_2)$ be a function. 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