Dear Colleagues,

We continue our Colloquium in the Math Department.

Lucas van der Merwe,
Dept. of Mathematics,
University of Tennessee at Chattanooga

Thursday, April 1, EMCS 422, 3:00 pm.

Criticality Index of Total Domination

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 $G$. We define the \it{criticality index} of an edge $e \in E(\overline{G})$ as $ci(e)=\gamma_t(G)-\gamma_t(G+e)$. Let $E(\overline{G})=\{e_1,\dots,e_{\overline{m}}\}$ and let $S=\sum_{j=1}^{\overline{m}}ci(e_j)$. Then the \it{criticality index} of $G$ is $ci(G)=S/\overline{m}$. We determine the criticality index of cycles.



Lucas van der Merwe
Department of Mathematics
University of Tennessee at Chattanooga
phone: (423) 425-4564