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Friday, November 10, 2017 - 15:45 to 16:45
Math Conference Room
Sudeep Stephen
The University of Newcastle, Australia
Zero forcing in graphs
Abstract: For a two-colouring of the vertex set of a simple graph $G=(V,E)$, consider the following colour-change rule: a red vertex is converted to blue if it is the only red neighbour of some blue vertex. A vertex set $S\subseteq V$ is called \emph{zero-forcing} if, starting with the vertices in $S$ blue and the vertices in the complement $V\setminus S$ red, all the vertices can be converted to blue by repeatedly applying the colour-change rule. The minimum cardinality of a zero-forcing set for the graph $G$ is called the \emph{zero-forcing number} of $G$, denoted by $Z(G)$. This concept was introduced by the \emph{AIM Minimum Rank -- Special Graphs Work Group} in~\cite{AIM-2008-Zeroforcingsets} as a tool to bound the minimum rank of matrices associated with the graph $G$. In this talk, I shall give an overview of the zero forcing problem along with some of the results that we have obtained during my Ph.D candidature. To conclude, I shall state few open problems that I intend to tackle along with my mentors while in NISER, Bhubaneswar.

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