+91-674-249-4082

Submitted by klpatra on 6 November, 2017 - 09:52

Date/Time:

Friday, November 10, 2017 - 15:45 to 16:45

Venue:

Math Conference Room

Speaker:

Sudeep Stephen

Affiliation:

The University of Newcastle, Australia

Title:

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.

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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