Lecture of György Kiss

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Published on 2021. szeptember 12. vasárnap, 21:20

Resolving sets and identifying codes in finite geometries

The Department of Geometry is pleased to divulge that

György Kiss
(ELTE, Budapest, Hungary & University of Primorska, Koper, Slovenia)

gives a lecture at the Kerékjártó Seminar with title

Date and place of the lecture is:

Abstract of the lecture:
Let $\Gamma=(V,E)$ be a finite, simple, undirected graph. For $u,v,s\in V$ let $d(u,v)$ denote the distance of $u$ and $v,$ and let $N[s]$ denote the closed neighborhood of $s$.

• A vertex $v \in V$ is resolved by $S=\{v_1,\ldots,v_n\}\subset V$ if the list of distances $(d(v,v_1),d(v,v_2),\ldots,d(v,v_n))$ is unique. $S$ is a resolving set for $\Gamma$ if it resolves all the elements of $V$.
• A subset of vertices $D\subset V$ is a dominating set if $V\subset \bigcup_{d\in D}N[d]$.
• A vertex $s$ separates $u$ and $v$ if exactly one of $u$ and $v$ is in $N[s]$. A subset of vertices $S\subset V$ is a separating set if it separates every pair of vertices of $G$.
• A subset of vertices $C\subset V$ is an identifying code for $V$ if it is both a dominating and separating set.

In this talk resolving sets and identifying codes for graphs arising from finite geometries (e.g. Levi graphs of projective and affine planes and spaces, generalized quadrangles) are considered. We present several constructions and give estimates on the sizes of these objects.

Here are some snapshots of the event:

• Current program of Kerékjártó Geometric Seminar.
• About the Kerékjártó Seminar.

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