Dear Colleagues,

We continue our COLLOQUIUM at the Math Department.
 
Lucas van der Merwe*, Marc Loizeaux, and Francesco Barioli

Department of Mathematics

University of Tennessee at Chattanooga, Chattanooga, TN, USA

Thursday, May 8, EMCS 422, 2:45-3:45

A Family of $4$-Critical Graphs with Diameter Three

Abstract. Let $\gamma_t(G)$ denote the total domination number of the graph
$G$. $G$ is said to be total domination edge critical, or simply
$\gamma_t$-critical, if $\gamma_t(G+e)<\gamma_t(G)$ for each edge $e\in
E(\overline{G}).$ In this paper we study a family $\cal H$ of $4$-critical
graphs with diameter three, in which every vertex is a diametrical vertex,
and every diametrical pair dominates the graph. We also generalize the
self-complementary graphs, and show that these graphs provide a special case
of the family $\cal H$.

* The speaker.

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Boris P Belinskiy
Colloquium Committee

Department of Mathematics, Dept. 6956
University of Tennessee at Chattanooga
615 McCallie Avenue
Chattanooga, TN 37403-2598
Ph. (423) 425-4748
Fax (423) 425-4586