@article{, AUTHOR = {Klostermeyer, William F. and Mynhardt, Christina M.}, TITLE = {Secure domination and secure total domination in graphs}, JOURNAL = {Discuss. Math. Graph Theory}, FJOURNAL = {Discussiones Mathematicae Graph Theory}, VOLUME = {28}, YEAR = {2008}, NUMBER = {2}, PAGES = {267282}, ISSN = {12343099}, ABSTRACT = {A \emph{secure} (\emph{total}) \emph{dominating set} of a graph $G=(V,E)$ is a
(total) dominating set $X\subseteq V$ with the property that for each $u\in
VX$, there exists $x\in X$ adjacent to $u$ such that $(X\{x\})\cup\{u\}$ is
(total) dominating. The smallest cardinality of a secure (total) dominating
set is the \emph{secure} (\emph{total}) \emph{domination} \emph{number}
$\gamma_{s}(G)$ ($\gamma_{\operatorname{st}}(G)$). We characterize graphs with
equal total and secure total domination numbers. We show that if $G$ has
minimum degree at least two, then $\gamma_{\operatorname{st}}(G)\leq
\gamma_{s}(G)$. We also show that $\gamma_{\operatorname{st}}(G)$ is at most
twice the clique covering number of $G$, and less than three times the
independence number. With the exception of the independence number bound,
these bounds are sharp.}, }
