id: 06072544
dt: j
an: 06072544
au: Sheikholeslami, S.M.; Volkmann, L.
ti: Signed total $\{K\}$-domination and $\{K\}$-domatic numbers of graphs.
so: Discrete Math. Algorithms Appl. 4, No. 1, 1250006, 11 p. (2012).
py: 2012
pu: World Scientific, Singapore
la: EN
cc: 
ut: signed total $\{K\}$-domatic number; signed total $\{K\}$-dominating
    function; signed total $\{K\}$-domination number; signed total
    dominating function; signed total domination number
ci: 
li: doi:10.1142/S1793830912500061
ab: Summary: Let $k$ be a positive integer, and let $G$ be a simple graph with
    vertex set $V(G)$. A function $f : V(G) \to \{\pm 1, \pm 2, \ldots ,
    \pm k\}$ is called a signed total {$k$}-dominating function if
    $\sum_{u\in N(v)} f(u) \ge k$ for each vertex $v \in V(G)$. A set
    $\{f_1, f_2, \ldots , f_d\}$ of signed total $\{k\}$-dominating
    functions on $G$ with the property that for each $v\in V(G)$, is called
    a signed total $\{k\}$-dominating family (of functions) on $G$. The
    maximum number of functions in a signed total $\{k\}$-dominating family
    on $G$ is the signed total $\{k\}$-domatic number of $G$, denoted by
    $d^{t}_{\{k\}S}(G)$. Note that $d^{t}_{\{1\}S}(G)$ is the classical
    signed total domatic number $d_{S}(G)$. In this paper, we initiate the
    study of signed total $\{k\}$-domatic numbers in graphs, and we present
    some sharp upper bounds for $d^{t}_{\{k\}S}(G)$. In addition, we
    determine $d^{t}_{\{k\}S}(G)$ for several classes of graphs. Some of
    our results are extensions of known properties of the signed total
    domatic number.
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