منابع مشابه
$k$-tuple total restrained domination/domatic in graphs
For any integer $kgeq 1$, a set $S$ of vertices in a graph $G=(V,E)$ is a $k$-tuple total dominating set of $G$ if any vertex of $G$ is adjacent to at least $k$ vertices in $S$, and any vertex of $V-S$ is adjacent to at least $k$ vertices in $V-S$. The minimum number of vertices of such a set in $G$ we call the $k$-tuple total restrained domination number of $G$. The maximum num...
متن کاملUpper k-tuple domination in graphs
Department of Mathematics, National Taiwan University, Taipei, Taiwan Taida Institute for Mathematical Sciences, National Taiwan University, Taipei, Taiwan National Center for Theoretical Sciences, Taipei Office, Taiwan LaBRI UMR CNRS 5800, Univ. Bordeaux, Talence, France Department of Mathematics Education, Catholic University of Daegu, Kyongsan, Republic of Korea Department of Mathematics, Sh...
متن کاملRoman k-Tuple Domination in Graphs
For any integer $kgeq 1$ and any graph $G=(V,E)$ with minimum degree at least $k-1$, we define a function $f:Vrightarrow {0,1,2}$ as a Roman $k$-tuple dominating function on $G$ if for any vertex $v$ with $f(v)=0$ there exist at least $k$ and for any vertex $v$ with $f(v)neq 0$ at least $k-1$ vertices in its neighborhood with $f(w)=2$. The minimum weight of a Roman $k$-tuple dominatin...
متن کاملk-tuple total domination and mycieleskian graphs
let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...
متن کاملk-TUPLE TOTAL DOMINATION IN INFLATED GRAPHS
The inflated graph GI of a graph G with n(G) vertices is obtained from G by replacing every vertex of degree d of G by a clique, which is isomorph to the complete graph Kd, and each edge (xi, xj) of G is replaced by an edge (u, v) in such a way that u ∈ Xi, v ∈ Xj , and two different edges of G are replaced by non-adjacent edges of GI . For integer k ≥ 1, the k-tuple total domination number γ ×...
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ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2017
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2017.v13.n4.a1