Dear Colleagues,

We continue our Colloquium.

Teresa W. Haynes,

East Tennessee State University,

Christine Mynhardt,

University of South Africa,

Lucas C. van der Merwe

University of Tennessee at Chattanooga

Tuesday, April 8 , Metro 212, 2:00pm.

Total Domination Edge Critical Graphs with Minimum Diameter

Abstract}. A set $S$ of vertices of a graph $G$ is a total dominating
set if every vertex of $V(G)$ is adjacent to some vertex in $S$. The
total domination number of $G$, denoted by $\gamma_t(G)$, is the minimum
cardinality of a total dominating set of $G$. 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 $e\in E(G)$. For
$3_t$-critical graphs $G$, that is, $\gamma_t$-critical graphs with
$\gamma_t(G)=3$, the diameter of $G$ is either 2 or 3. We study the
$3_t$-critical graphs $G$ with $diam G=2$.