Zobrazeno 1 - 10
of 125
pro vyhledávání: '"{K}-DOMINATING FUNCTION"'
Autor:
Lutz Volkmann
Publikováno v:
Opuscula Mathematica, Vol 44, Iss 2, Pp 285-296 (2024)
Let \(k\geq 1\) be an integer, and let \(D\) be a finite and simple digraph with vertex set \(V(D)\). A weak signed Roman \(k\)-dominating function (WSRkDF) on a digraph \(D\) is a function \(f \colon V(D)\rightarrow \{-1,1,2\}\) satisfying the condi
Externí odkaz:
https://doaj.org/article/fbea9ae4603849dea666fa19227275ef
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 43, Iss 1, Pp 115-135 (2023)
For positive integers j and k, an efficient (j, k)-dominating function of a graph G = (V, E) is a function f : V → {0, 1, 2, . . ., j} such that the sum of function values in the closed neighbourhood of every vertex equals k. The relationship betwe
Externí odkaz:
https://doaj.org/article/421e4cc1c0d5443f9b5a3eb431a28bb6
Publikováno v:
AIMS Mathematics, Vol 6, Iss 1, Pp 952-961 (2021)
Let $G$ be a simple graph with finite vertex set $V(G)$ and $S=\{-1,1,2\}$. A signed total Roman $k$-dominating function (STRkDF) on a graph $G$ is a function $f:V(G)\to S$ such that (i) any vertex $y$ with $f(y)=-1$ is adjacent to at least one verte
Externí odkaz:
https://doaj.org/article/54b7b8ea339c4d36a7511caaad284fbd
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 39, Iss 1, Pp 67-79 (2019)
Let k be a positive integer. A signed Roman k-dominating function (SRkDF) on a digraph D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) Σx∈N−[v]f(x) ≥ k for each v ∈ V (D), where N−[v] is the closed in-neighbor
Externí odkaz:
https://doaj.org/article/0c70d0535d794c4fa357d9a2506a6de3
Autor:
L. Volkmann
Publikováno v:
Communications in Combinatorics and Optimization, Vol 3, Iss 2, Pp 173-178 (2018)
Let $G$ be a graph with vertex set $V(G)$. For any integer $k\ge 1$, a signed (total) $k$-dominating function is a function $f: V(G) \rightarrow \{ -1, 1\}$ satisfying $\sum_{x\in N[v]}f(x)\ge k$ ($\sum_{x\in N(v)}f(x)\
Externí odkaz:
https://doaj.org/article/70529953f3554966ae89fb20085f2cc3
Autor:
Volkmann Lutz
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 37, Iss 4, Pp 1027-1038 (2017)
Let k ≥ 1 be an integer. A signed total Roman k-dominating function on a graph G is a function f : V (G) → {−1, 1, 2} such that Ʃu2N(v) f(u) ≥ k for every v ∈ V (G), where N(v) is the neighborhood of v, and every vertex u ∈ V (G) for whi
Externí odkaz:
https://doaj.org/article/ad75caa012e041a3bd30e7a811cdad97
Publikováno v:
Discussiones Mathematicae Graph Theory, Vol 37, Iss 1, Pp 39-53 (2017)
Let k ≥ 1 be an integer, and G = (V, E) be a finite and simple graph. The closed neighborhood NG[e] of an edge e in a graph G is the set consisting of e and all edges having a common end-vertex with e. A signed Roman edge k-dominating function (SRE
Externí odkaz:
https://doaj.org/article/df4852dc8318467293ed59ddce985c42
Autor:
A. Mahmoodi
Publikováno v:
Communications in Combinatorics and Optimization, Vol 2, Iss 1, Pp 57-64 (2017)
Let $k\geq 1$ be an integer, and $G=(V,E)$ be a finite and simple graph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph $G$ is the set consisting of $e$ and all edges having a common end-vertex with $e$
Externí odkaz:
https://doaj.org/article/10c99c78b871468982a9680384b5b47b
Autor:
N. Dehgard, L. Volkmann
Publikováno v:
Communications in Combinatorics and Optimization, Vol 1, Iss 2, Pp 165-178 (2016)
Let $D$ be a finite and simple digraph with vertex set $V(D)$. A signed total Roman $k$-dominating function (STR$k$DF) on $D$ is a function $f:V(D)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\i
Externí odkaz:
https://doaj.org/article/9dcb22611e7041b1ad9c0d87eb97e54a
Autor:
N. Dehgardi
Publikováno v:
Communications in Combinatorics and Optimization, Vol 1, Iss 1, Pp 15-28 (2016)
For any integer $k\ge 1$, a minus $k$-dominating function is a function $f : V \rightarrow \{-1,0, 1\}$ satisfying $\sum_{w\in N[v]} f(w)\ge k$ for every $v\in V(G)$, where $N(v) =\{u \in V(G)\mid uv\in E(G)\}$ and $N[v] =N(v)
Externí odkaz:
https://doaj.org/article/7de48aec39ab42949a4220881124425a