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 = {267-282},
ISSN = {1234-3099},
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 $u\in V-X$, 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.},