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<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-size:12pt;font-family:"Times New Roman","serif"">Sayın liste üyeleri,<br></span></i></p><p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""> <span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-size:12pt;font-family:"Times New Roman","serif"">MSGSU
Matematik Bölümü Genel Seminerinde bu haftaki konuşmacımız Sibel Özkan. Seminer
ile ilgili tüm detaylar aşağıda yer almaktadır. </span></i><span style="font-size:12pt;font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""> <span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">Sibel Özkan
, Gebze Teknik Üniversitesi<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""> <span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">Başlık:<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">On
Domination Number of Cayley Graphs</span><span style="font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""> </span><span style="font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">Özet:<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">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.<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;font-family:"Times New Roman","serif"">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.<span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-family:"Times New Roman","serif""><span> </span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif"">Tarih: 27 Şubat Perşembe 2020, 16:00</span><span style="font-family:"Times New Roman","serif""><span></span></span></p>
<p class="MsoNormal" style="margin:0cm 0cm 10pt;line-height:115%;font-size:11pt;font-family:"Calibri","sans-serif""><span style="font-size:12pt;line-height:115%;font-family:"Times New Roman","serif";color:black">Yer: Matematik Bölümü Seminer Odası</span><span style="font-family:"Times New Roman","serif""><span></span></span></p><p class="MsoNormal" style="margin:0cm 0cm 0.0001pt;line-height:normal;font-size:11pt;font-family:"Calibri","sans-serif""><i><span style="font-size:12pt;font-family:"Times New Roman","serif";color:black">Seminerde görüşmek dileğiyle,</span></i><span style="font-family:"Times New Roman","serif""><span></span></span></p>
<br clear="all"><div dir="ltr"><i>Fatma Altunbulak Aksu</i><div><br></div><div><span style="color:rgb(0,0,0);font-family:"Times New Roman";font-size:medium;font-style:italic;text-align:center"></span><br></div></div></div>
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