[Turkmath:4343] MSGSU Matematik Bölümü Genel Semineri- Sibel Özkan- 27 Şubat Perşembe 2020, 16:00

[FATMA ALTUNBULAK AKSU]

*Sayın liste üyeleri,*



*MSGSU Matematik Bölümü Genel Seminerinde bu haftaki konuşmacımız Sibel
Özkan. Seminer ile ilgili tüm detaylar aşağıda yer almaktadır. *



Sibel Özkan , Gebze Teknik Üniversitesi



Başlık:



On Domination Number of Cayley Graphs



Özet:

A {\em dominating} set of a graph $\Gamma$ is a subset $D$ of $V$, such
that every vertex not in $D$ is adjacent to at least one member of $D$. The
{\em domination number} $\gamma(\Gamma)$ is the minimum cardinality of a
dominating set for $\Gamma$. The problem of determining the minimum number
of queens that can be placed on a chessboard so that all squares are either
attacked by a queen or are occupied by a queen is considered as the origin
of the study of dominating sets in graphs. Concept of the domination number
is defined for the first time -although with the name ''coefficient of
external stability"- in Berge's graph theory book from 1962. There are over
two thousand academic papers and several books on the topic since then.



Let $G$ denote a finite group with identity 1 and let $S$ denote an
inverse-closed subset of $G \backslash\{1\}$. The Cayley graph Cay($G;S$)
of the group $G$ with respect to the connection set $S$ is the graph with
vertex-set $G$, in which $g \in G$ is adjacent with $h \in G$ if and only
if $h=gs$ for some $s \in S$. The definition of Cayley graph was introduced
by A. Cayley in 1878. It is related to many practical problems, and also to
some classical problems in pure mathematics.Since finding the domination
number is NP-complete for arbitrary graphs, it is natural to ask for bounds
on the domination number related to other graph parameters, and also to ask
for exact results on specific graph classes. Here we will focus on Cayley
graphs. There are limited results on the domination number and finding
efficient dominating sets on Cayley graphs on certain groups for certain
connection sets. Here, we carry these investigations further and also study
different types of dominations. Results given in this talk is due to joint
works with Cafer Caliskan and Stefko Miklavic, carried under the TUBITAK -
ARRS bilateral project with project number 115F586.



Tarih: 27 Şubat Perşembe 2020, 16:00

Yer:  Matematik Bölümü Seminer Odası

*Seminerde görüşmek dileğiyle,*

*Fatma Altunbulak Aksu*

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