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Neighbor-distinguishing k-tuple edge-colorings of graphs
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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...
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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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1976
ISSN: 0095-8956
DOI: 10.1016/0095-8956(76)90010-1