Dear Colleagues,

We continue our Colloquium in the Math Department.

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Thursday, November 18, EMCS 422, 3:00 pm.

Lucas van der Merwe and Marc Loizeaux,

Department of Mathematics,

University of Tennessee at Chattanooga

$4_t-$ Critical Graphs with Maximum Diameter

Abstract

Let $\gamma_t(G)$ denote the total domination number of the graph $G.$ A
graph $G$ is said to be total domination edge critical, or simply
$\gamma_t-$critical, if $\gamma_t(G+e)<\gamma_t(G)$ for each edge in
$E(\overline{G}).$ We show that, for $4_t-$critical graphs $G,$ that is,
$\gamma_t-$critical graphs with $\gamma_t(G) =4,$ the diameter of $G$ is
either 2, 3 or 4. Further, we characterize structurally the $4_t-$critical
graphs $G$ with $diam G=4.$

Significant portions of this talk will be appropriate for students.

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Boris P Belinskiy

Department of Mathematics, Dept. 6956

University of Tennessee at Chattanooga

Ph. (423) 425-4748